The open source tools are good for development/testing but won't be able to synthesise your hdl to produce a bitstream, you'll need to use one of the manufacturers tools from altera or xilinx (or others).
The manufacturers tools come as suites , are large (5GB install and need 7 to 12 GB drive space) available for windows and linux. altera.com xilinx.com
There are plenty of soft cores out there.
opencores.org would be a good place to have a look at
There is the zpuino which is arduino compatible.
Best idea is start simple and build up
Get a fpga board, implement a simple design (led flasher) and work up from there.
Quite a learning curve especially if you haven't done much digital electronics.
Remember its hardware and your designing circuits not writing code
so timing is everything.
Have a look at the fpga4fun.com projects and work through them
as a starting point.
xilinx based
digilentinc has some low cost boards , as does gadget factory.
avnet has a usb dongle based board for $80.
altera based .
terasic has some nice boards.
Gadget factory has a kickstarter project up at the moment for the paillio + a few addon boards http://www.kickstarter.com/projects/13588168/retrocade-synth-one-chiptune-board-to-rule-them-al