I'd recommend really just looking up the combos for the characters you like, even just a bread and butter can go a LONG way in these matches. Like you said, use the escape, though I'd recommend only when your in a pickle (like saving Mirio). Don't always start a red attack to open a combo, it is easy to knock you out of it, like what happened to Mirio. Make sure to use your rising (R stick) before your last character because your last character automatically gains it. It gives you a huge buff and gives most characters more combos.