The problem with Inquisitor is that it is a very swift action intensive class and the mythic abilities are also often swift or immediate actions. I'd probably go with heirophant just for the flavor, and inspired spell will not conflict with your swift actions. But depending on the choices you made for your character, hierophant may not have a lot of good path abilities for you.
Take a look at the Mythic Hero's Handbook which has Inquisitor-specific content.
Legendary Games has produced a lot of mythic content and their stuff is pretty much top-notch.
Well, since you have a high crit range weapon, you can hardly go wrong with champion and fleet warrior so that you can move and full attack in the same round.
The typical alternative is to go with a mythic vital strike build, which doesn't need a specific path. While that combined all of the normal damage of your iteratives into a single hit- which means you blast past DR with sheer huge numbers- you lose out on the multiple crit chances of a normal full attack. You also lose out on extra attacks like haste.
You may want to consider dual path and take hierophant for your second path. Inspired spell allows you full access to your spell list which is a huge advantage for a spontaneous caster. Later the Hierophant can take enduring blessing to make a single spell last all day. Having a constant heroism gives you a nice boost on almost everything. If you pick up mythic heroism it becomes even better. Those two abilities alone are enough justification for taking dual path.
Without knowing your characters build giving advice on path abilities is a little difficult. If you are going for the typical intimidate focused inquisitor Menacing Presence is always good. Many inquisitor use their inquisition to use WIS for their social skills instead of CHA. The thing to be careful about if you are doing this is that many of the marshals path abilities are based on CHA. If your character is doing this you will want to avoid choosing these abilities
Way of Knowing is another universal path ability that works well for an inquisitor. It does not help with combat but getting a 6th level spell that is not on your list that allows you to more easily track down your opponent is always a good thing.
Mythic power attacks is kind of a waste since you are already using a two handed weapon. Spending a mythic point to gain a +2 bonus to hit on melee attacks is not really all that good. If you took dual path you could spend a mythic point and gain heroism for 70 minutes instead even if you don’t have heroism on your list of spells known.
I would still go with dual path. Inspired spell is just too good for a spontaneous caster to ignore.
If you are going for the face role Persuasive Countenance is the obvious choice for path ability. Taking Hierophant will also allow you to pick up Divine Countenance. They should stack but check with your GM to make sure. If so you can get a shift of two categories on someone who is within one step or your alignment before you even use any social skills.
Keep in mind that you are not a full BAB class so your access to some combat feats will be delayed. Use your lower levels to boost other aspects of your character until you qualify for the combat feats.
Inspired Spell (Su): You can expend one use of mythic power to cast any one divine spell, treating your caster level as 2 levels higher. This spell must be on your divine spell list (or your domain or mystery spell list) and must be of a spell level that you can cast using that divine spellcasting class. If you are a spontaneous spellcaster, you don’t need to have the spell prepared, nor does it need to be on your list of spells known. Using this ability does not expend a prepared spell or available spell slot. You can apply any metamagic feats you know to this spell, but its total spell slot level must be a slot level you can normally cast.
The inquisitor has a lot of good spells. More spells than you'd ever be able to add to your spells known.
Yeah, Inspired Spell is a must have for divine spell casters. You're getting good advice here.
By my count there are over 90 1st level inquisitor spells. Depending on the sources you have available to you, your count may be more or less than this number. The number of spells on the list goes down as the level rises. The list of 6th level spells is still over 30 spells. As a spontaneous caster you can learn a very limited number of these spells. The normal maximum number of spells known for an inquisitor maxes out at 6 per spell level. A couple of races can go slightly above them number by using their FCB to gain extra spells known. But even then you are limited to about 9. That means that as an inquisitor you can learn 7% -10% of the spells on the list. Inspired spell gives you access to the other 90% of your list.
You can use magic items to cast the spells you don’t know, but that takes resources. You also have to plan out what spells the items have in advance. Inspired spells uses mythic points which are a renewable resource that cost you nothing. Not only does it give you access to the spells it increases the number of spells you can cast per day. At tier 1 you get 7 mythic points that can be used to cast 7 extra spells per day. If nothing else that is 7 more times you can cast divine favor. Mythic power attack at your level would grant you the same increase to hit, by negating the penalty to attack, but would not increase your damage above what it is already doing. Divine favor would add an additional +2 damage. That makes mythic power attack a lot weaker. Using heroism instead of divine favor is going to be even stronger. Now you get a +2 bonus on all attack rolls, saves and skill checks and it lasts for 70 minutes at your level.
What makes the inquisitor so powerful is the ability to stack bonuses. Inspired spell gives you access to a lot more thing you can combine.
Inspired spell is very, very strong.
That said I happen to have theory crafted a inquisitor which was a mythic marshal. but he was an archer. So I might have some useful input here. Who knows.
Top tip for anyone thinking about making a mythic character that fights with weapons.
The legendary weapon/items universal path abilities, are very, very nice. Foe biting is nasty, especially for a crit fisher/vital strike build.
Mythic spell casting would also be nice :) for example mythic Heroism is very strong.
Depending on party comp, shatter resilience could be nice. Perfect Aid + Heroic block can be a very nice combo for your buddies.
Make Heirophant your main choice, and dual path into Champion for damage (you can max your damage on a crit, etc - tons of damage dealing choices here). If going full on 10 mythic ranks, the DR 10/- that Heirophant gets is pretty solid capstone (plus other goodies too).
Inspired Spell - think about what you might be able to do if you go with a multiple ranks in Divine Source (Universal Path ability starting at rank 3) as well as having your Inquisitor spells ready as needed? The flexibility is huge.