Going from a starting point of their tentative steps in Unchained, here is what I hope to see with various combat actions under the new action economy and skill rules. I know I may not get all my wishes, but hopefully they don't go with the least interesting most restrictive option in every instance. Like with the basic attack equivalents point below, I hope they go with some version of that, and not just "You must always hit your enemy with your metal stick, no tactics for you."
-----
Mixed Movement: Movement should be combined proportionately, because part of what an action should represent is time spent. If you have a land speed of 20 and a swim speed of 40, you should be able to walk 10 ft then swim 20 ft as one action. I know they are defining Stride, Swim, Fly etc as separate actions, but they really should combine in this way for continuous movement, without having to waste your turn just because you got to a wall you really could have kipped over to press an assault.
Guarded Step: Since the successor to the "5 foot step" is now an actual action taking a few seconds, instead of a simultaneous free action occupying less than a second, it should actually allow you to move 10 ft. This would open up a lot of tactical space. It also opens design space for things like ancestry or other feats to give more movement on a guarded step, and if an effect halves your movement speed it can now also halve your Guarded Step speed.
Open Door, Pick Up Object, etc: These should only waste actions unto themselves if you're not moving. I can see not wanting to spend movement to do these so you set yourselves apart from 5E, but at the very least, while you're moving you should get one "free action" to perform these activities.
(Honestly, I'd just make it cleaner by always freely giving one bonus action per turn for trivial "actions" like this. Dare I say it... a "swift action," as it were.)
-----
Minimize which attacks Provoke: Maneuvers should not provoke... or at least not if you're trained in the skill (seemingly mostly Athletics) used to make those attacks; no feat tax should be required. Ranged weapon attacks, touch attack spells, and ranged touch attack spells should only provoke if you are actually targeting someone at range, and thereby ignoring your surroundings. If you use such a weapon or spell to attack someone in your melee reach, you should be considered to be on guard and therefore should not provoke.
Basic Attack Equivalents: Whenever something gives you a bonus "basic one-action weapon attack," such as an Attack of Opportunity, you should be able to substitute in any other attack defined in the Combat chapter that you can perform as a single action. I won't go so far as to say that you should be able to use one-action special attacks granted by feats and class abilities in this way (although that wouldn't actually bother me). What I'm actually referring to are the other basic options like shove, trip, etc - all the basic attack options you can attempt in a single action. Those at least should be options whenever you have a bonus attack, whether said attack is acquired due to AoO, Haste, or whatever else.
Two-Weapon Fighting: What I'm currently expecting is that without taking any feats, you can at least switch up attacks with multiple weapons without taking any kind of penalty. To actually start getting bonus attacks though - actual two-weapon fighting as known in prior editions - you'll have to probably take a feat chain. This may operate like Unchained, where TWF lets you use one of your actions each turn to make attacks with both weapons (probably requiring Expert weapon proficiency), Improved TWF lets you do this with two actions each turn (likely requiring Master weapon proficiency), and Greater TWF lets you do this with all three actions (likely requiring Legendary weapon proficiency).
We know there is a Double Slice feat. In PF1, this lets you add your full ability modifier on damage with TWF with your off-hand weapon. That's kind of weak, but they said this was a powerful option for the Fighter. So, I'm seeing a couple ways this could go. Maybe base TWF halves your ability modifier with both weapons and not just the off-hand weapon, and Double Slice thus significantly increases your damage output by restoring your full ability modifier to damage for both weapons. Or maybe it is now an entirely different feat that actually gives the Fighter a TWF action of some sort while actual TWF is reserved to other classes like the ranger. In this latter instance, maybe Double Slice acts as Rend in PF1 - if you manage to land hits with two separate weapons, you get to roll for bonus damage? Hm.
Called Shot: Please give a functional Called Shot option in the core book that we can playtest. At the very least, it'd be nice to see some consistent rules for dealing with tentacle monsters and other such circumstances where the player would logically think to try to attack the long appendage that is grabbing onto them.
Iterative Attacks: Just taking this opportunity to propose again that PC attacks should work the same way as monster attacks, namely: primary attack at +0, all subsequent attacks at -5. I know it's going to be +0/-5/-10 in at least the playtest rulebook but I HAVE to push for this, haha...
-----
Feint: Feint should be a single action. Hopefully this allows you to choose whether you are rolling Bluff, Intimidate or Sleight of Hand "Thievery" against the target's Sense Motive, instead of restricting you to only Bluff. Improved Feint would then potentially be something like letting you use a reaction to convert a failed attack roll to a Feint, or alternately letting you Feint multiple people at once.
I mentioned this elsewhere, but: I would like to see the Rogue get Trick Attack, like in Starfinder. This would be explicitly defined as a better, ranged version of Feint, and as such would be a good option for the Rogue to impose flat-footed on an enemy so they can use their Sneak Attack for bonus damage without needing a flanking ally nearby. As a result, any feats applying to Feint would also apply to Trick Attack. It feels like I'm unlikely to get this, but I'm at least going to reiterate how much I want it. This is an option that really plays up how the Rogue is the designated skill monkey class.
Shove, Trip, etc: So, we know these mostly use Athletics to attack. I assume this is against a target number of 10 + the higher of the target's Athletics or Acrobatics rating. Since Pathfinder 2 will presumably remain crunchier than Starfinder, I'm hoping there's still a size modifier to these sorts of attacks and defenses... just please let it be less than 4 per size difference.
Please please please DO NOT give the target a ridiculous +8 bonus to their defense against maneuvers like in Starfinder, that just completely locks maneuvers out as viable options. I also have to reiterate that I hope none of these actions provoke, at least if you're trained in the skill you're using to make the attack. I like seeing maneuvers in combat at my table, but if the ability to attempt them without fear of reprisal is locked behind feat taxes again we'll be right back to PF1.
Dirty Trick: It would be interesting to see this as a two-action Bluff or Thievery based option against the target's Sense Motive to replicate any other one-action maneuver without having to use Athletics. As a bonus rider, you impose a condition for 1 round on a hit or a worse / longer duration version of that condition on a crit. Somehow I doubt they'll go this route, but that does seem like a cool way of handling it to me.
Grapple: Two actions to initiate, two actions to continue on subsequent turns with the option to spend additional actions on more Grapple sub-actions. In terms of book layout, Grapple should be its own heading in the combat chapter with separate subactions listed under it as their own paragraphs for maximum clarity. Maybe this will FINALLY be the one true D&D clone to actually get grappling right and make it easy to understand for everyone, so it's not a giant chore every time it comes up.
Do not give monsters a "Grab" action that works separately from Grapple. Monsters and PCs should use the same rules here. "Attach" and so on work somewhat differently and that's fine, but Grab should not once more become the be-all and end-all of useful monster tactics. The only circumstance in which I would be okay seeing Grab is if it is defined as a bonus to Grapple checks, like, Grab +4 for a monster that gets +4 on its Grapple attempts.
-----
Delay: IF this is still in the game, please make it EXCEEDINGLY clear that you CANNOT delay only part of your turn: it's all or nothing. Even with this being explicitly the rule in PF1, my players still try to delay part of a turn all the time, no matter how many times I correct them. This may be one of those rare situations where A WHOLE SENTENCE IN ALL CAPS is actually called for in the rulebook, to really drive the point home.
Control Minion: I totally accept having to spend an action to give pets, summoned monsters and other minions commands of what to do. But once you've given them those orders, they should at the very least get to continue acting on those orders every turn until you give them new orders, without having to burn an action for this every turn. Your pet wolf shouldn't just stop and start licking herself while face to face with an enemy because you didn't devote an action to commanding her that turn.
Concentration: Concentrating on an ongoing effect can just take one action. Easy. Actively directing an ongoing effect, like moving your Flaming Sphere somewhere, can take an action of its own... or possibly just get rolled into the concentration action.
Terminology: This has bothered me before, but it really stuck while writing the grapple section above. Can we... clear up the terminology around actions and things with action in their name? Hell, go full on video game and say each character gets "3 AP" per turn with various "maneuvers" or whatever costing 1-3 AP each. That way I don't have to say a Grapple Action takes Two Actions and lets you take X, Y and Z Actions inside your Grapple Action.