It's possible, but most would recommend having an EJ207 shortblock installed instead. Has factory forged internals which the EJ257 doesn't, and is often done under your budget.

You can have your current EJ205 heads serviced and mounted on an EJ257 block, which would mean your existing manifold/wiring/ancillaries will all bolt on and plug in with no issues. The later model heads/wiring loom/intake manifold etc that a 257 usually runs is not plug and play with a 2000 WRX, you can convert the car to run them but will blow your budget unless you're doing all the work yourself. Running your existing heads on a 257 with no other changes will result in a compression ratio that is too high; some use a thicker head gasket to counter this, or you can buy dished pistons to bring the compression ratio down. A weakness of the standard EJ255 and EJ257 is the pistons suffering ringland failure, they are not a factory forged item - going aftermarket forged & dished pistons would counter this.