This depends on the kind of experiments you want to run. I recommend the Virtex 2 boards if you're doing small logic. If you're doing something complex target for Virtex 5, especially if you need an on-ship processor for serial calculations. I think it comes with PowerPC. If you can provide more detail for your experiment I can help you chose a better FPGA.
An ALU is Arithmetic Logic Unit were you do all the "math" stuff: addition, shifts, multiplication, etc.
You program them using HDL software, either VHDL or Verilog. The latter is more C-like. I prefer the first. I have worked with it a long time. You can download Modelsim student edition and experiment with it.
Its not easy learning FPGA so take some time to learn how to program HDL first.