I'm 5'4", 140 male. I ride a 125, but it is a bit on the tall side - I only get one foot down. I would not have been comfortable doing it if I was a new rider, but I rode for 10+ years when I was a kid.
The TTR255 or CRF230 would be the ideal starter bike for you IMHO. However, those are not really suitable for an MX track. Thus, the 125 2 stroke MX bike would be the logical choice given your $$ limitations and size/weight.
It will take you a little while to get used to using the clutch and keeping it "on the pipe" but I would think you would get the idea within a couple rides.
If the 125 MX'ers seem to tall, you can cut the seat foam and gain an inch or so. You can also cut the rear subframe (that the seat mounts on) and gain 1/2 inch to an inch that way.
When properly set up, the bike should sag under your weight (amount = 4 inches sag with you on it as compared to when it is sitting on a crate with the rear wheel off the ground) - thus, when ideally set up, it should sit maybe 2 inches lower than when its parked with no one on it.
So . . . you can gain almost 2 inches with minor mods to the seat and subframe, and it should sit maybe 2 inches lower when you sit on it than when you're not.
I bought a 2002 RM 125 last year for $1500. That was a really good deal, but I would think you could find something year 2000 or 2001 for that price pretty easily.