making the transition from KoF to Skullgirls

I suggest you to play solos until you learn the characters. Understand what each character can do and learn how to behave on neutral.
You can check the BnB compendium for combo references and the character specific forums for more in-depth knowledge and discussion.

Play matches against people! And not just in quick match. Find a lobby, or perhaps play some sets with some people here! It's a good way to really learn a thing or two, plus you'll make some friends along the way!

While learning combos and being able to execute them is indeed important, there are many other aspects of SG that are just as essential if not more so. Learning how to play at neutral, what to do in certain matchups, how to utilize assists properly, as well as how to mixup and reset the opponent (and when to do so) are just a few things that are important to consider as well.

Spend some time practicing in training mode, but don't spend all day there! Learning how to execute a combo and actually using it in a match are very different beasts. When you're just starting out and learning basic combos, don't worry about damage! Combo consistency is much more important at this stage, plus there are a lot of other things to learn and focus on.

Feel free to add me on PSN. I usually play on PC, but I'm on my PS3 fairly often and will respond to messages and game invites.

This is coming from a guy for has played KoF for the past 10 years, throw any KoF logic out of the window in this game.