The first thing I did was missions when i got the game. I didn't even get passed the first one for any of the characters I play, so i decided to just go with the flow and see what happens. As I've said before, I'm really lousy at getting the timing down right to get hits to combo into each other. It doesn't help that I still so used to UMvC3 where it's so easy to just connect hits and jumps are safe, which is one thing that screws me over alot in here and in 3rd Strike.
Easiest way to start with combos in Kof is to begin with combos using command normals after a normal and then into a special or super move. Easy and a great hit confirm.
So with Ryo you can do sHP or sHK, forward+LP, either of the supers.
The sequence becomes even easier with Ryo because the fireball super's motion overlaps with the forward+LP so all you have to do to get the combo is:
HP or sHK, forward+LP, hcf+P
Remember to hold punch down after you do the special move. This goes for any special move in the game, always hold the button down after doing it. This way the game remembers the input for about 5 frames and repeats it for you.
With Terry its even easier since his close HP hits for two hits so you have a long time to confirm if it connected and enter a special or super.
With Ryo it would be easiest to combo with sHK because it has a huge cancellation window on it, its so large in fact that it feels like you can pretty much link his faster moves after it (so it can act as a single hit hit-confirm).
Both with Ryo and Robert you can use this simple combo for good damage, its probably one of the most used combos with Ryo overall because of how fast his crouching HP is:
down HP, fireball, super
The motion becomes easy because of overlap so you just do:
down HP, qcf+P, hcf+P (supercancels into the fireball super)
down HP, qcf+P, hcb+P (supercancels into the ranbu super)
Same applies to Robert, he also has command specials he can add after normals. His Forward+LK has a really big buffer window so you can enter a special way ahead of time and have it come out.
Robert's BnB meterless punish is sHP, forward+LK, hcf+K