Bankroll management is one of the hardest things in poker because the swings we can experience when playing no limit holdem is insane. When playing other variants like potlimit then the swings are not so big as we won't be losing our whole buyin with one bad beat. When I first started out with poker I went up the buyins too quickly and ended up going broke a few times. It's best too play dynamically with our bankroll, so as soon as we lose a few buyins it's best to lower our stakes again.
Building a serious bankroll without any starting money is very difficult. Freerolls are usually full of players, so even if you can win 10 or 15 USD it comes down to number players. If you are competing with thousands of other players than your chances are very slim. In my opinion it's better go look for a good casino with 100 or 200% deposit bonus. Like that you have already a good balance to start with.
Good luck with your challenge.