So really what is the best way to start a bankroll? Is it to deposit cash and play well, hoping to not lose that money? Or is it to try continually to win freerolls and work up from $2 and $3 wins?
depends if you have the resources, if you are able to deposit $50 or so that will not hurt you to lose, that way would probably be worth it. But if you are unable to deposit any money, free rolls/selling play chips is the only thing you can do.
If you only have $2 or $3 to work with, you're going to need some luck to not lose it. There's just too little to work with in order to develop any sort of bankroll. In general, I think you should try to start out with $50 or so as long as you can afford it. Otherwise just keep rolling the dice and hope you get lucky at one point or another.
I really think you have to deposit money. You don't want to be playing with scared money, so deposit enough to cover yourself at the levels you want to play.
If you can't deposit too much, make sure you play within your limits. Busting your roll can be very frustrating. Do what you can to stay out of that type of situation.
Absolutely agree with TenBob's comment. Save up $100-$200 and then deposit (hopefully you get a bonus with it). If you are new to online poker grinding small stakes SNGs is a decent way to build up the BR, but if you want to be a cash game hero, go for it.
I recommend depositing $50 and taking it to the nl50 HU tables and hoping for the best or you could do the whole "Bank roll management" thing and keep your $$ for a few weeks at least.