I like the looks of the 05 Neon. Saw an 02 yesterday while I was out and hadn't seen one in awhile.
Compare the price of that rebuild with some of these modern marvels like Ford's Power Shift. Or a Jatco CVT. Or GM's 6 speed. It will put it in perspective. Is this the three speed? Or did Dodge offer the 4 speed by that time in the Neon?
I have put obscene amounts of money into "worthless" cars because I love them and don't get rid of them.
If you plan on keeping this car for another 100,000 miles, get the rebuild. If not, then a used one with low mileage would be a better move. Either way you'll be better off than being chained to a 72 month loan with a $500 payment on something newer.
Good luck with this. I'd love an 05 Neon and even considered one after my car was totaled in a rear ender.