fpga4fun.com

Yes, an FPGA is ideal for capturing quadrature signals into binary counter and feed that to your PC. 32-bits counters are not a problem (just take more space into the FPGA). You can use any of the PC interfaces that you mention. For example, RS232 is good (if speed isn’t an issue). You need to create a small protocol, controlled by a state machine, so that the 14 channels are muxed out to the PC, with maybe a double-buffer scheme since transmission isn't instantaneous...

Now since you are an FPGA novice, your best shot might be to try a few simpler FPGA designs first, and go from there!

Downloading a compiler with a simulator might be a good way to find out if it is too complicated or not.

Setting up a simulator and writing testbenches has its own learning curve. I would put that in step #2. First step should be fun, without simulation, just "play" with an FPGA. Write a few lines of code, load them, see the result, change the code, etc...

That depends on if you think it is worth wasting $100 to find out. If you don't factor in the money about the money then I agree.

If fun is important then I would reccommend a far cheaper microcontroller that is well capable of such a task unless the frequencies are too high.