If you're just starting out then I wouldn't suggest any type of cash game. With such a small bankroll it would be a lot easier for a lot of folks to just play freerolls with an occasional low buyin tourns like something like 10 cents to 25 cents buyin.
Even if you play a game with a $1 max buyin in a cash game you could go up $1, then lose 2 buyins or worse, then get that" I have to get it back mentality" and the whole bankroll will be put in jeopardy. So I wouldn't suggest playing cash games with your bankroll.
You just wouldn't give yourself enough room with some aggressive donk beginner moves on you and you'd more than likely get frustrated and go higher limits or keep playing when you should quit.
You don't want anything that if you lose your buyin would psychologically make you feel like you have to chase lost money.
You don't want to be thinking "It took me xyz amount of hours, days, weeks, lol months to get something and now I just lost it" lol. Even if you haven't destroyed your bankroll then when you have that mentality without DISCIPLINE then I CAN ALMOST GUARANTEE THE REST OF THAT MONEY IN THE ACCOUNT WILL BE GONE AS WELL.
Regardless of your route whether cash game or tourn, you also want a tourn something that you could easily replace the money whether the money comes from an outside source like your piggy bank or you can win it back and you know from experience that its easy to replace.
So I'd say stay away from cash games and play tourns or sngs with an occasional small, really small buyin that wouldn't bother you if you lost the money.
IF you're just playing freerolls and small, uber small buyins relative to your bankroll like the example of the 10/25 cent buyin with a $20 bankroll then you shouldn't go broke if you replace the paid buiyin with freerolls.
But putting a big chunk of your bankroll on the table every time you play is a recipe for going broke even if you were the greatest player in the WORLD playing donkey beginners just because of variance.