Hi, sorry this is late but I don’t have a PC at home, and it’s a pain in the butt to type long paragraphs on my phone at home. Off the top of my head here are some tips:
Zangief: There was a VERY VERY GOOD Gief player named XTG up here (now in TX), and I have played Boxer v. Gief probably more than any other match in Super Turbo. The matchup is so INTERESTING imo, I still to this day don’t have a strong opinion on who wins this matchup, I think it’s probably 5-5 because I just feel that it is completely up to who is the better player…but then when I lose HARD 10 in a row it is of course easy to think, this matchup is horrible. 
Anyways, I low rush ALL DAY (nothing but jab low rush of course), from a good mid-spacing. Kick rush can beat lariat reliably, but sometimes you will just get smacked out of it, too. You can go backwards and whiff short kick rush, and if you see him start a lariat, do kickrush super to cleanly beat lariat, but straight punch super loses to lariat every time.
If you don’t have a charge, never try to instead trip lariats. On blocked greenhands you can throw, but I prefer cr. MP>Low Rush to punish. The situation you most want to avoid is a knockdown because Gief can safejump and then do SPD/FAB BS on you, and there is nearly nothing you can do. If you wakeup and reversal headbutt, he will block and you will be punished HARD, if you get knocked down in the corner you’re pretty much dead (as you should be). If you get knocked down midscreen and Gief safe jumps or is right next to you, I often just hold up/back and pray, even if you get hit once or twice but remain alive, you might live to fight another day, and it’s better than being SPD’d or FAB’d.
Guile: I think of this match as three seperate matches per round: 1) The first 0.5 seconds of the round, 2) After part 1 is finished, the part where Guile retreats and you now have to get in, and 3) You getting in (if Guile doesn’t kill you during step 2).
In the first 0.5 seconds of the round, if Guile starts with an immediate sonic boom, your st. Fierce will beat him cleanly, and even if you’re a little late, you will trade and both be knocked back a bit (but you win on damage, so even that ‘tie’ leaves you ahead). However, if he starts off with a flash kick immediately, it will beat low rush or the st. Fierce Punch. So I either start with st. Fierce, kick rush >throw/headbutt, or do nothing and try to jump over a boom or basically “react” to what he does.
For step 2), this is obviously the hardest part, because you are playing Gilly’s game. I try to not get cute with J. Neutral Fierce over booms (Jump straight up, and press forward+FP over a sonic boom to advance a little bit instead of jumping towards over it). The time I will J. Neutral Fierce is when I think Gilly will boom, then jump forward and try to air-to-air me, because J. Neutral Fierce is way better air to air than jump forward fierce. Try to neutral jump over booms a lot so that Guile doesn’t “train” you to jump forward into a bad situation, you want to be jumping forward safely, which means you are a bit off of the ground by the time Guile is booming. You need to play this matchup against a really good Guile for a long time to get the feel of when it is safe to jump forward. You can also jab headbutt through booms too. If you get meter and are fullscreen, if Guile throws a slow boom you can of coarse do short kickrush>super to punish, but that is very rare for them to make that mistake.
Step 3) Killing Guile when he’s in the corner (much harder to do in HDR due to improved Flashkick): This is not that different from every other character. He is going to crouch in d/b, and you have to jump in when he booms incorrectly and kill him with j. RH, cr. MK/MP>Low rush, or when he is scared to pull the trigger you short kick rush>throw, or kick rush>headbutt to beat when you think he will counter throw.
Chun Li: This matchup starts very similar to Guile in that your st. Fierce at the start of the round will beat any of her fireballs. What I find REALLY hard to deal with is if she spams lightning legs a hair’s breadth in front of you, because you cannot walk backwards due to proximity block (or whatever it’s called), and you can’t jump attack her, and she can stop anytime and instantly cr. mk or throw. I think J. MP is your best air-to-ground when she does this, because the hard buttons sure don’t work well. I would try to always avoid this range against her because of how good fireball, lightning leg, and cr. mk or walkup mini-SPD are. It is better to stay at midrange or even far range against Chun Li than be up in her face IMO.
From fullscreen it is great to bait her into a fireball war, because Chun Li players might not realize you can beat her fullscreen even if you don’t have a fireball. If she FB’s fullscreen you can beat or trade with her with mp straight rush,and you will win HEAVILY on damage, beware of dizzies though. Also from fullscreen you should short kick rush forward, and easily visually confirm if she fireballs and then you can super through it to punish.
I’m rushing to type this up before work, if you have more specific questions, shoot away!
