Anti airs
MP shoryuken - invincible, highest damage and most reliable
cr. HP - Good from close but not as reliable as stopping crossups as SF4. Must be done slightly preemptively.
HK - anti airs from disturbingly far away, but pretty lousy up close
jump back LP/LK - good for AAing if they jump very close to you, where all other AAs fail.
MP shoryuken xx CA - If you have the meter to spend, a good way to land super.
Parry into follow up - Not guaranteed to hit the opponent grounded or airborne, not guaranteed to be a punish, and opponent can just empty jump throw. Builds a bit of v-meter. Not recommended.

Note that EX shoryuken works as an anti air but adds negligible damage compared to the MP version. It might be better at anti airing divekicks such as necalli d+HK


Punish combos
st. MP, cr. HP xx HP shoryu (244 damage, 395 stun) - general punish combo, quick and damaging
st. MP, cr. HP xx MK tatsu (212, 395) - less damage, more corner carry. HK tatsu crosses up so not recommended here.
f+HP, st. MP, cr. MK xx MK tatsu (254, 410) - Higher damage, slower. Again, the oki and corner carry of MK tatsu are superior here. Uppercut doesn't reach in this combo. 

Note that Ryu has no way of using 1-2 bars to meaningfully increase his punish damage outside the corner.

st. MP, cr. HP xx HP shoryu xx CA (454, 395) - most damaging way to go into critical art most of the time. 


Punish combos USING V-trigger

st. HP xx trigger, cr. HP xx HP uppercut (266, 469) - Note that this punish doesn't work on crush counter punishable attacks, so use the superior st. HK starters against those.
st. MP, cr. HP xx trigger, (slight walk) cr. HP xx HP uppercut (284, 511) - This is slightly more optimal but significantly harder. 

Punish combos using v-trigger and super are usually wasteful since it throws away the whole v-trigger bar for slightly more dizzy, but if you do want to do them it's just add CA on the trigger combo's ending uppercuts.


Crush counter punishes:

st. HK, cr. HP xx HP shoryu (280 475) - the most reliable combo since it requires no walking. 

You can actually walk in slightly after a point blank st. HK crush counter and get any of his st. MP punish combos above. The walk is not as precise.

far HK, (walk) cr. MK xx MK tatsu (221 430) - If you're far away this is a practical ender. You can also go for a f+HP cr. MP punish to far away attacks

Ryu's cr. HP is extremely narrow so you have to walk in slightly following a neutral jump or crush counter punish to get the link.


Ranged Punishes

cr. HK (90, 150)
CA (300, 0)

Ryu actually kind of sucks at this. Super and sweep are pretty much it from what I can tell. st. MK xx v-trigger, st. MK or st. MK xx v-trigger, sweep are probably your highest damage punish options w/o super.


Confirm combos

Ryu's st. MP which starts a lot of his punishes also starts his confirms. The only useful confirm combos besides far st. MP confirms where cr. HP is impractical.

st. MP, cr. MK xx MK tatsu (185, 350)
st. MP, cr. MK xx CA (345, 190)


Confirm combos (light normals)

cr. LK, st. LP, st. LK xx MK tatsu (141, 329) - a 3 lights confirm, somewhat rare among the cast. Shoryu won't reach here
cr. LK, cr. LP xx HP shoryu (159, 293) - Higher damage but less reaction time
cr. LK, st. LP, st. LK xx LK tatsu, CA (307, 329) - super version of first combo
cr. LK, cr. LP xx HP shoryu xx CA (369, 293) - super version of second combo


Non CC punish CC confirms 

CC st. HP xx st. HK (171, 252) - basic meterless followup to successful st. HP
CC st. HP, CA (378, 180) - Only works from somewhat close. You can v-trigger to make it work at all ranges


counter hit BnBs
CH st. MK, st. LK xx MK tatsu (179, 343) - You can pick up this link on a counter hit st. MK which isn't too hard to get but it doesn't work from the furthest reaches of st. MK.
CH cr. MP, CA (342, 120) any counter hit cr. MP can be followed with a reaction super. Feels like SF3 Ken cr. MP link super but easier.


corner stuff
st. MP, cr. HP xx EX hadou, EX shoryu (324, 495) - You can do combos into EX fireball then EX shoryu in the corner. The damage is OK but 2 bars is a lot.


midair connect and juggles

anti air fireball, CA (330, 100) - Ryu can quite easily super on reaction to the opponent landing on a fireball. This works from really far away and is even easier in v-trigger

j. MP, b+HK (116, 211) - this is ryu's best hope at a meterless follow up.
j. MP, j. MP xx HK tatsu (196, 305) - this is insanely impractical right now but might get more viable on release. You need a crazy deep j. mp.
j. MP, EX shoryu (224, 280) - this is the BnB 1 bar follow up
j. MP, CA (350, 100) - BnB super follow up
j. MP (1 hit) xx tatsu, HP shoryu (166, 230) you can still preserve the free juggle state with a cancel to tatsu on first hit, but it's more impractical because tatsu has more ground recovery and HP shoryu is slower. You could go into sweep too I guess.