A TTR125 is not cheap those are about 1200. Now that is pretty cheap for a dirt bike but I doubt you know how to ride a clutch. But if you think you are up to the challenge of a clutch then go right ahead. But i suggest something from Honda. Maybe a Honda CRF80F. Now those are clutches too but there easier to start on. That's what i started on with a clutch. I highly recommend that. Then i would go to a Honda CRF100F or if you grow faster then go to the Honda CRF200F those actually aren't that much taller than the Suzuki 125.
If you want a cheap bike mine as well go for a mongoose
Ebay
craigslist.com
eBay
at lowriders.com
I'd start with a dirt-cheap MTB. It's most likely to be made of a steel alloy that's not too hard to weld motor mounts and stuff to.
you don't!!
everywhere
Haro
You wont be able to find a quality bike that is also cheap. If you want a quality bike check out www.performancebike.com.
Probably the easiest way to buy a cheap bike is to look for one at local garage sales or flea markets. There is also several websites where cheap bikes can be found, for example eBay.
First make sure the bike is in neutral and push kick start down on right side of the bike.