One important thing to look at when first going to a casino and seeking lower limit games is to consider the rake. In most casinos in the USA, the rake is a fixed percentage with a "cap per hand", for example: 5% with a maximum of $4. That means, when the pots is less than $80, you pay the maximum rake of 5%, so low limit games have a more expensive tax.
A great example in the old days was the $1-$3 Stud games at Foxwoods. The rake was so high, it's difficult for anyone but the house to win in that game. I used to challenge myself by sitting in that game and *just* trying to keep an even stack, which was tough to do!
Frankly, too, $60 is not going to be enough for most games at Casinos. The previous poster is right that you have to find a 1-2 fixed limit for that to be enough at all.
I started playing 2-4 fixed limit HE, and needed about $600 to avoid "going broke", and even then, I "went broke" once and had to replenish my bankroll.