So I am going to start a Pathfinder adventure path for the first time. I am not a first time GM. So what I was wondering was which of the adventure paths has a good amount of roleplay involved and which ones use mythic tiers? I know Path of the Righteous has mythic tiers involved but I was curious if any of the others do. I am trying to avoid any that seem like they are focused on combat because I know my players want to do a lot of RP. Thanks for any input.
Unfortunately I cannot speak to a great deal of experience with the adventure paths concerning having actually played through them (I've gotten 1/2 of the way through Skull and Shackles, 1/2 of the way through Curse of the Crimson Throne, am currently 4/6 of the way through Rise of the Runelords, and have finished Wrath of the Righteous) - I can say that I have read through and understand the plot of a majority of the APs.
What's really fantastic about Paizo's Adventure Paths is that they can really be tailored to fit any group's style, with plenty of room for lots of combat and the ability to skip the dialogue for groups who prefer to play that way, and on the flip-side, really reading into the campaign can lead to lots of roleplay opportunity, especially for perceptive and (in my case) obsessive GMs.
I think instead of thinking of the APs in a combat versus roleplay sense, you really should look at the theme of the APs to help you decide what you want to play.
P.S. Wrath of the Righteous is the only AP with mythic heroes (though AP's going forward will include mythic rules here and there I believe). I really recommend if you or another plan to run this campaign you (or they) look into the numerous threads about adjusting the campaign, as it unfortunately suffers from a lack of sufficient mythic testing.
Any adventure path can be retrofitted to use mythic rules, though Reign of Winter actually has a possible suggested "continue the path" that encourages mythic rules.
The end of Serpent's skull also makes a good deal of sense if it uses mythic rules.
As for roleplaying, while it is true that it is possible (and easy to do) in all of the APs, some push towards it more strongly than others:
1) Curse of the Crimson Throne is the front runner on this one. The AP spends most of it's time in a city, where roleplaying is easily more prevalent than combat. Even when it's not in the city there's tons of roleplaying with barbaric tribes. When adventure (#5) is entirely a dungeon with not much RP so you may need to tailor a solution around that.
2) Council of Thieves - again an urban AP, this one has a strong emphasis on roleplaying in several parts of it, the most outstanding of which is the second adventure, where the party has to act through a particularly murderous stage play in a devil worshiping country, and the play itself is provided in the adventure in case you actually want to play it out.
3) Carrion Crown has tons of roleplay during most of it - the players interact with the suspicious citizens of a horror stricken country filled with werewolf, undead and even Lovecraftian beasties. The first half of the AP in particular is very roleplay heavy.
4) Wrath of the Righteous is very focused on the entourage of NPCs who support the characters. Differently from the other APs I mentioned here the roleplay in this one is less a nessecary part of the story, but the seeds are certainly there for a GM to cultivate
Those I'd say are the four APs with the most focus on roleplay hardwired into them. Virtually all other APs have some wonderful RP elements to them as well, and a GM could always expend on the adventures - if you haven't read an AP yet you'd be surprised at how many little things you read there will inspire you to create your own stuff and add to the game.
also what Lord Snow said, I would add mythic is broadly considered a failure (or at least a failure from tier 3 onwards). Check out the wrath of the righteous threads there's lots of information there. If you're looking for mythic feeling I do think the best solution is to be generous in the use and allotment of hero points as this can capture that heroic feeling without too much work or ramifications.