If you're just interested in leveling the class storylines, it doesn't matter what server you're on. You're not going to be grouping with people because there's no point (unless you want to do a daily Flash for the 10 comms). If you're doing the story, you won't want people talking while you're watching the movies anyways if you're like me so you'll turn voicechat off and won't read chat. The class storylines was the only real 'solo' part I considered when people talked about SWTOR being a 'single player game'. The rest of the leveling was just like any other MMO.
So, if you don't have longterm plans for TOR, any server will do for that. Storylines vary as to taste, so might want to find out which one you think you'll be interested in. By all accounts, Sith side are infinitely better than just about any Pub one.
edit: For Pub, I think Jedi Covenent is a bit more active than Shadowlands.