Well, I have yet to beat gouki on the easiest level with 15 or so continues, so I can empathize with your problem.
The game is hard, but from my experience, the first opponent on level 1, no matter who, is usually very passive and hardly blocks. I'd be aggressive against the first opponent. Jump in with fierces and roundhouses. Don't worry about blocking on the first guy. I don't even think you have to use any special moves, just jump in roundhouse, sweep roundhouse.
After the first few opponents, if you are getting pummelled by jumping in, let them initiate the action. Learn your guy's effective anti-air moves and do an occassional low sweep when they are walking towards you. Even if they block, at least you slowed down their attack.
If you're having trouble with jumping in, you may be timing your kicks or punches a little too early or a little too late. Experiment to figure out the timing in different situations. For example, you can press short or jab very early in the jump and it will hit, but with very little damage. Forward or strong can usually be pressed a little later and the damage will be greater than the short/jab. Fierce and Roundhouse must be timed more precisely but do the most damage. To me, jumping in with punches tend to have less range, and therefore, you face a higher probability of getting hit.
Also try to time your jumping in right after you have knocked them down. They usually won't be able to counter early enough and if they block, at least you can get some tick damage.
Guile's jump in forward and Zangief's jump in down fierce (looks like a belly flop, not the swinging arm thing) are good moves to jump in with at any time.
Although I haven't noticed set patterns, there are tendencies that you'll eventually notice. For example, Ken and Chun-Li jump in a lot. When Ryu jumps in with a roundhouse, you must block it or you will be swept by a roundhouse, without a doubt. It is almost as if it were the next sequence of the same animation. You must block high and low very quickly. Avoid being too predictable with throwing fireballs etc. at honda and blanka or when it appears that they are holding down+back/defending low/charging. They will do their special moves and land on your head.
The four new characters are all hard and blanka and honda are bastards against fireball type players. The four bosses are pretty much the same as the previous versions and the game actually gets easier once you get to them.
I know nothing about playing against human players, but from what I've seen/read/heard, jumping in is not recommended.
As hard as the game is, it's so much fun. I have played it everyday for a month and today was the first time I saw honda's qcb+strong or fierce throw. Keep playing and it'll get easier, at least until you get to akuma/gouki, whatever his name is.
Hope this helped.
Longtime lurker, first time poster.
Kurt
