Face

Normals
2A - Really fast, chains into other stuff. Not a low though.
2B - Really good range, hits low, and cancels into specials. You will use this a lot.
5B - Somewhat slow but cancels to 5D, making it an ideal low mixup starter.

f.C - Okay poke, gives decent frame advantage.
2C - Solid Anti-Air. Has a weird hit-box though, so you may end up trading. Gets solid combos from it though.
6C - Overhead. Kind of slow and nothing comes off it, but does decent damage and is good for mixups.

2D - Big Slide. Really unsafe on block, but you can space it to make it unpunishable against some characters.

j.B - Big Cross Up.
j.D - Knocks down.
Chains
2A 2B
2A 5B
2A 2C
5B 5D
Best low option. Easy to hit confirm into damage.

Heat Up Only Chains

2B 2C
2B 2D
Specials
Gun Chains: 236P, 214P, 623P, 236K Can chain up to 3 in a row with some restrictions. All Gun Chain shots force standing on hit.

236A/C - Frontier Shot
Rolls forward and shoots. Awkward at first, but very good range and very useful.
Can be faked by holding the P button. Can be useful for throw mixups and baiting Gatchis.
Has a somewhat low profile, so it can avoid certain attacks. Can roll under Cedric and Odile's projectiles clean. Profile remains low longer if the move is faked.
C version has more startup, but rolls farther and deal a lot more hitstun, so more combos are possible.
Can be canceled into Bazooka, or any other Gun Chain moves.
214A/C - Wild Comeback
Rolls backward and then returns forward with a shot. Super useful poke, can be used for a lot of things, like baiting throws or attacks. Causes more hitstun that Frontier as well. Good for building meter too. C version is slower but causes even more hitstun.
Can be faked by holding the P button. Very useful for throw mixups.
Can be canceled into any other gun Chain move.
┕▶ 623A - Middle West (Fast)
Can only be done from Frontier or Wild Return.
An overhead shot with very good range. Very fast but low damage. You can link a Bazooka off it with good timing. On some characters you can link a B Texas Knee off it on hit.
┕▶ 623C - Middle West (Slow)
Can only be done from Frontier or Wild Return.
Very slow and rolls forward before attacking. Does a LOT of damage, but knocks down and is generally pretty useless.
┕▶ 236B/D - Grand West
Can only be done from Frontier or Wild Return.
A low shot with good range and speed. Seems to be fairly punishable on block. Can be canceled into Bazooka but that's it. Not exceedingly useful but nice to have every now and then.
D version is slower but knocks down.
623B - Texas Knee (Light)
Super fast, hits a big area. Can be comboed after. Can cross up on knocked down enemies. Is throw invincible on startup. Can be thrown on block though so don't spam it. One of Face's most important moves just because of the speed of it. Expect to be using this one a lot.
623D - Texas Knee (Heavy)
Slower and doesn't travel as far forward as the light version, but it's a much stronger finish. You should use this version only at the end of combos, when you can.

Supers

236236A/C - Wilderness Bazooka
A fast projectile attack. It's completely invincible on startup and very fast. It's also pretty darn safe most of the time. However, it only has to be parried once so it's not good to use on a whim.
A version travels diagonally upwards, C version travels strait forward.
236236B/D - Raging Revolver
It usually does very low damage and can easily miss, but is relatively safe and you can use it to chip people to death in some situations. It damage scales better in combos as well, so many combos are actually stronger to finish with it than with the Bazooka.
B version travels a short distance and D version travels farther.
Heat Up
During Heat Up, Face loses all of his Gun Chain specials but gains a new set of shots. These shots are lightning fast, hit the entire length of the screen, and can be juggled into each other.
They also do more damage the closer you are to the enemy.

236A - Quick Draw (Mid)
Shoots a strait forward shot at head level. Good for catching out of the air at a distance or in juggles. Cancels to any other shot or to Super.
236C - Quick Draw (Low)
Shoots a strait forward shot at foot level. Hits low. Very good surprise attack and combo starter. Cancels to any other shot or to Super.
214A - Quick Draw (High)
Shoots a shot diagonally upward. Does the most damage of any shot. Cancels to Mid or Low shots, or to Super.
214C - Quick Draw (Over)
Does a short jump and shoots diagonally downward. Hits High. Somewhat slow so easy to block on reaction, but can be a very good surprise attack, and can be used to leap over fireballs and other things. Doesn't cancel into anything, but juggles the highest so is the easiest to follow up on.
Shot Damage Ranking:
High > Mid > Over > Low

Enhanced Normals

5D - Causes Wallsplat on hit.

Enhanced Chains

2B 2C
New low chain in Heat Up. Can chain into gun shot combos. Becomes your ideal 'low' starter because 5D allows them to tech quickly.
2B 2D
Another new chain in Heat Up.
Combos

Basics

623B, 623B
623B, 623D
Only works in the corner, or anywhere on Freed.
(Corner)
623B, c.C
Reset, mixup as they come down.
2A 2B 623B, 623B/D
2A 2B 236A 236236C

5B 5D 623B, 623B/D
5B 5D 236A 236236C

(Corner)
c.C 623B, 623D
c.C 214A 236A (236236C)

AA 2C 236[A], 623D

CH 2C/5D 214A 236A (236236C)

236C 214A 236A (236236C)

214C/236C 623A, 623B, 623B/D
Difficult to connect, only works on some characters or in certain situations.
... 623A, 236236C
Tight link off overhead shot into Bazooka. Tricky, but very useful and easy to hit confirm. May miss if distance is too large.
214C/236C 236B (236236C)

CH 214C 236C 214A (236236C)

(Corner)
CH 214P/236C, 623B, 623D
Not really hit confirmable so not that useful.
CH 214A or 236A:
Gives access to same combos as 214C and 236C

Gatchi Counter

GC c.C 623D
[956]
GC c.C 623B, 623D
[1228]
GC c.C 214A 236A 236236C
[1457]

High Gatchi Drive

(0 Any)
44, D 236[A], 6, c.C 236[A], 623D
[941]
(0 Any)
6 (cross under) c.C 236[A], D 236[A], 623D
[944]
Very slightly more damage but a little harder to do. Use it to put them behind you instead of in front of you.
(0 Back to Corner)
66 (cross under) 623B, 5D 623B(1), 623D
[992]
(0 Near corner)
j.C |> 236A 214C 236C, 623D
[1097]
(0 Mid to Near Corner)
j.C |> 214C 236C 214C, 623D
[1168]
Won't work deep in the corner on some characters.
(1 Any)
j.C |> 214C 236C 236236D
[1231]
(1 Near corner)
j.C |> 236A 214C 236C 236236D
[1416]
May work anywhere on some characters (Deathbringer)
(1 Mid to near corner)
j.C |> 214C 236C 214C 236236D
[1487]
Won't work deep in the corner on some characters.
(2 Mid)
Heat Up, 44 f.C, 66 c.C High Mid High Mid High Mid 236236A
[1753]
(2 Near Corner)
Heat Up, j.C |> 6, c.C, 6, 5D High Mid High Mid High Mid 236236D
[1841]

(1+ back to corner)
Heat Up, 2 (cross under) 2C 623B, 5D High Mid High Mid High Mid, 623D or 236236D
[1361/1757]
Gets you out of the corner and them into it.

Low Gatchi Drive

(0 Any)
66 66, c.C f.C 2C 623B, 623D
[1288]
(1 Mid)
66, j.D |> 5B c.C f.C 236A 236236C
[1507]
(1 Corner)
66, c.C f.C 2C 236A 236236C
[1468]
(2 Any)
Heat Up, 66 66, c.C f.C 2C Low Mid High Mid High Mid 236236D
[1968]

Note: 2C can miss on some characters sometimes, especially Olivia/Odile. For these characters, you can substitute c.C f.C 2C with j.D |> 5B c.C f.C.

Heat Up

2B 2C Low High Mid High Mid High
(Corner)
2B 2C Low Mid High Mid High Mid, 623D

2B 2C 623B, 623B, 623B/D
(Corner)
2B 2C 623B, c.C 623B(1), 623D

2B 2D

AA 2C, Low Mid High Mid
(For very high AA)
AA 2C High Mid High Mid
(Near Corner)
AA 2C High Mid Over, 66 623D

5D, Mid Over, Mid High

(Mid)
... 623B, 623B, 623B

(Any)
Low Mid Over, Mid Over, High
(Any)
Low High Mid High Mid High
(Any)
Low Mid High Mid High Mid (236236P/K)

(Any)
Mid Over, Mid High Mid High

(Any)
Over, Mid Over, Mid Over, High
(Any)
Over, Mid Over, Mid High Mid (236236P/K)

(Corner)
Low Mid Over, Mid Mid Over, 66 623D
(Corner)
Low High Mid High Mid Over, 66 623D
(Corner)
Over, Mid Over, Mid, Mid Over, 66 623D
(Deep Corner)
Low Mid High Mid High Mid 623D

(3-shots near corner)
Low Mid Over, 66 623A, 623D
(3-shots near corner)
Over, Mid Over, 66 623A, 623D