I agree with the post of Adamchikas, it depends on your goals. If building a bankroll is the goal, it is difficult, but not impossible to start with $3 or even nothing. Pokerstars
offers a lot of freeroll satellites for the weekend Round Two freeroll, which offers a purse of $250 and pays out to several hundred spots. I say if you can win a spot and then cash in the weekend tourney, you can start on your way. After all, if you can't win at that level, you will have little luck putting your own cash up.
It's been said you can't make a living playing in tournaments, you have to play in some cash games. But even the penny/two penny games require almost a buck to get in. With a $3 bankroll, you've got no staying power and also will play shy. You need more reserves than that. So I would advise playing the freerolls until you build up a little bigger bankroll, then start in the small cash games to start building up your cash and points.