I would strongly recommend the multi-table sit and go's.
1) very low buy-in's so your bankroll will last longer.
2) smaller fields than MTT, so a better chance of making the later stages and see how a larger tournament would develop.
3) lower variance compared to MTT's
4) softer fields that cash games
5) lower rake
Another tip; be fully prepared to lose your first deposit. Treat this as your training fee. Learn to play the game, handle variance and bad beats, bank roll management, game selection, etc, etc. $10 probably isn't enough, but obviously it depends on what you can afford to lose. You do not want to be playing with scared money.
If I were starting out from scratch again today, I would probably deposit $100. Enough to hurt a little bit, but not so much that I can't replace it with my next paycheck.
I wouldn't recommend freerolls and play money to learn how to play poker. Freerolls are great if you already have a good understanding of the game and looking to build a bankroll from nothing. Play money = waste of time.
Good luck with your poker adventure!