I'll probably be hitting an even mix of story mode and challenge tower for the first couple of hours so I can get a feel for how the final build flows. Once I've had a little time with all the characters, I'll narrow down the list to the 2 that appeal to me most.
After that, it's time for practice mode where I'll spend some time getting familiar with the auto combos and playing with some ideas. As far as long "show-offy" combo strings go, I'm not planning to spend much time learning them other than a few bread and butters just so I have something to punish mistakes with. Ideally, my approach to this game is going to be more centered around short, effective strings, psyching people out with dashing in and out, and zoning characters. That's obviously subject to change, though
As with most other people here, I am holding off with online play until I have some basic structure with my two "mains."