A used de0 nano would fall into your budget, but I think it makes no sense to buy it, now that the de10 nano is out
If you are starting with fpga, a higher end FPGA like the one on the de10 nano may not be the best approach.
A DE0 Nano has the advantage that many projects use it as a target because it has been out for a while, and a used one may be an affordable option.
I got a DE10-Lite (MAX10- based) it doesn't have as many free IOs as the DE0-Nano but has a larger but equivalent FPGA, and the same amount of SDRAM.
You can get 20€ boards from aliexpress, not the best but very affordable. I got 2 with a 10k LE Cyclone IV and one with a 16 k LE Spartan6. They work but they are pretty bare-bones.
Trenz electronics, here in Germany has many Xilinx boards, a few are affordable with a 100€ budget.