At your weight and circumstances, I'd look for a 250. The 144 has considerably more power than a 125, but you've got to keep it "on the pipe" as they say.
At 240lbs its going to be more difficult to do that. The 250 has much more "tractable" power and would be easier for you to learn on than a 125. (Note: Even though I'm recommending the 250, member "bclapham" had a 2002 RM 144 and he was 220 lbs if I recall - and he did race the 144 at very hilly Glen Helen - and he liked it a lot.)
Further, there are advantages to racing a 250. The 125 C/D classes tend to be filled with "crazy" 13-17 year olds who aren't all that worried about getting hurt - and thus may put you in danger.
Most of the time I race in open, unlimited or vet classes and occasionally do a 125C.
The 250 beginner class is not really going to be any faster than the 125's, but the riders will probably be somewhat older.
A disadvantage of the 250 is that it weighs 25 lbs more, but that shouldn't be a problem for you. The RM's tend to corner very well, the KX's tend to do very well in rough, straight line stuff and the CR's are the best combination of those two handling characteristics. The YZ's have had some of the best motors recently.
I found my bro a 2000 KX 250 for $1500 last May. I would think that if you're patient, you could find a 2000 or 2001 in good condition for the same price. A buddy got a 2001 CR250 for $1800 last September.
My .02 worth.