The alltrac is only AWD, the GT-4 is just the JDM name for them, you can usually call them an alltrac or a GT-4 and no one would mind. The 1990-1993 alltrac are all the same (minor differences), so you can include 1990 in your search. You will not find an alltrac for $2500, maybe a project car (mine is for sale for $3000) but not a running one, and definitely not a reliable one, if you want a reliable alltrac you need to spend about 9-10 grand. You can pick up a normal running-and-safetied one for about $5000.00
The FWD 'alltracs' are really just normal celica's with an alltrac motors (3SGTE) swapped in, and we usually call them 'Halftracs' they are also rare, you MIGHT be able to find one for $2500, but reliable might be a problem, cause they are swapped motors.
If you drop down to an 88-89 alltrac you might have a better chance finding one for $2500, but again it will need work.
You could probably pick up a Celica-needing-a-motor for $1000.00, and get an alltrac motor (3SGTE) for $1000 (tiger Japanese motors) and pay someone to put it in, but I don't know anyone who would do it for $500, but you would be getting close to your goal.
Ps. Welcome to the site.