So my dm sprung us goin mythic on us. I've never really looked into it before and was hoping for some guidance. Playing a gestalt spell sage wizard + mindchemist alchemist going into Pathfinder savant and Pathfinder chronicler. I also have Homebrew archetype on the wizard side delaying spellcasting for a ton more spellslots. Generally he is a support caster and skill monkey with an unhealthy love for potions and other consumables. Archmage seems the best path but I can't decide what to dual path into. What are the best abilities for my character? Are there any good feats besides dual path? What would be a good second path? Any guidance would be appreciated.
IMO dual path is only worth it if there are abilities from another path that you want. My necromancer took dual path because I wanted to grab the control the mindless path ability which only shows up under trickster. As far as feats go, most of the mythic feats are just improved versions of normal feats and actually have said normal feat as a pre-req. So, I would look at whatever feats you've already taken and see if there are mythic versions of those feats.
Their usefulness varies. Improved Counterspell (Mythic) is barely an upgrade, It lets you counter with spells of equal level. Where as Eldritch Heritage (Mythic) is substantial, as it gives you the rest of the bloodline powers (which normally you have to grab piecemeal, 1 feat per power, via improved and greater eldrtich heritage).
As a spellcaster of any sort you will probably want Mythic Spell Lore
If you have access to third party material, the Mythic Mania series of books greatly rounds out that which is missing from the original Mythic Adventures book. In addition, there is a path called path of the Genius which may be useful for your alchemist side. Otherwise, Archmage is the best bang for our buck on the arcane side.
Mythic Spell Lore is both a feat and a universal path ability, but it is limited to three times only on one side or the other. There is a path ability in Archmage for extra mythic spell power that makes absolutely no sense to take since it is limited to three times total and there is a universal extra mythic power path ability that just gives the same number of points of mythic power that can be used for anything, not just mythic spells.
Dual path takes up one of your five total feat slots, so unless you have a compelling reason to take a dual path, the only benefit of taking it other than access to both paths for choice of path abilities is the second basic path ability that is chosen during first tier from one of three options (it has a different name in each path). While there are not a lot of options feat wise for arcane casters in the base book, there is always the extra path ability feat that can net you additional path abilities which may make taking the dual path more palatable. There is also the universal path abilities and a spell caster with lots of mythic points and several selections of mythic spell casting ability can sling a lot of mythic spells each day.
As always, your mileage may very, so it is extremely useful to be as exact as possible in your goal so we the community can advise in a useful and targeted way.
There are plenty of good mythic feats. But much of it depends on your build.
Mythic Spell focus is pretty good for an offensive spell caster, as is mythic spell penetration. To get the most out of these you should have the greater versions.
The mythic version of iron will, lightning reflexes, and great fortitude are also useful for anyone with a weak save.
For an Archmage mythic spell lore will probably be the first mythic feat you take. It can be taken at any level and as you gain tiers it gives you additional mythic spells.