I have done FPGA work. The first thing you'll have to get around is that it is not "programming". You don't give the hardware a set of instructions to accomplish sequentially, you're actually attempting to describe hardware. The language you will use is referred to as a "hardware description language" for just this reason. I prefer Verilog as it is less verbose than VHDL, but everybody seems to have a preference of their own.
I usually use Xilinx hardware. You can get a S3E dev board for ~$100 from Digilent. You can easily get started with just a copy of ISE Webpack and a simulator.