Regarding execution things like doing quarter circle inputs or DP motions, it sucks but the only way to get reliable is to practice them in training mode until you have the muscle memory to do it, there's not much of a shortcut.
Regarding the game, PLAY THE WHOLE TUTORIAL FIRST before trying to play against people. The tutorial in skullgirls is one of the best tutorials in any fighting game and will definitely teach you the basics of what you need to know. After you've got that down then you can start looking for people to play against (playing single player against cpus can be helpful when you're just starting out but as in any fighting game if you play against the computer too long then you end up picking up habits that work against the computer but not people). Don't go on quick match yet though; find other beginners to play with. After "play the tutorial", "find people at your level to play against" is the biggest piece of advice I can give. Not only will you feel better because you aren't getting mopped every game, but having a group of people in the same situation as you will encourage you to improve (who doesn't love beating their friends?), which will make THEM want to get better, and so on.
As far as character selection, Fukua is a great character to start the game with. She's this game's "jack of all trades, master of none" and her combos are very easy compared to the rest of the cast (though no one in this game is THAT hard to learn so don't feel like you are stuck with just fukua if you decide later you want to learn someone else, you can).
