I got mine on ebay for under 250€ (with 4GB RAM and 240GB SSD, but it was used and not new)
But don't expect to be able to run every ps2 game at fullspeed with the NUC8i3 (God of War for example does only run with 30-45fps).
Alternatively AsRrock A300 with AMD Athlon 3000G or better Ryzen 3 3200G (but this will be a bit more expensive than 250€, i guess).
If it does not have to be "mini"-PC, then i would try to get a cheap used PC with components like Core i5 (at least Intel Haswell generation) and nvidia GT1030 or GTX 1050 or AMD Radeon RX 550/560 or better and at least 4GB RAM.
You should be able to find such a PC for about 200-250€ (maybe even less)
Here you can find a list of different PC hardware and the performance with Batocera: