I use one any time I do squats, but I usually try to go heavy. There are many different types out there. It depends on how much support you need. Right now, I am using a wider Nike belt, but have used the leather belts, and thinner belts, in the past. I would recommend just going to a sports store and trying them on to see how they fit you.
Actually you have probably strained your lower back, most likely spinal erector muscles. But you have to be careful with low back stuff, because if you really injure it, it can take a long time to heal. And its f***in miserable.
I would also recommend adding stretching esp. of the back and hamstrings if you're not doing so. Also, if your gym has a low back machine, start doing some very light sets on this, or just low back raises. If it starts hurting or even twinging your low back, just stop.
Regular NSAIDs, massage, heat, or even muscle relaxers can help.