Well, Elektronman,
By reading the posts I have to say that the suggestions really make sense. I am not going to say - making such board yourself is impossible, or so hard to do, or anything like this ...
There are different style of packages, and you certainly can get such that you can work with in your home lab. Two side PCB is not that hard to design, but keep in mind that you have to order it somewhere to be manufactured by professionals - such small tracks and small distance between tracks and vias cannot be made by hand or using printer and iron home brewing process.
I did one board my self, I know at least 2 or 3 similar boards made by my friends. All they work well. All are not professional, but are good / simple starter boards, however going to use it professionally is another story ...
Selecting a ready board is I think the best option. Then you will use time and energy really to play with the FPGA and to try to build the board. If I can share my opinion - sometimes it is so frustrating to try to make such a board yourself, so by the time and money you spend to get the board ready - you lose your will to play with it, which I think is your final goal.
If you don't have experience with FPGA, try to find a simple board, without much fancy options, just you need the FPGA, the memory, the programming port and some display option - leds, lcd display. By this you will make some experience and later when you know what exactly you want to do you will buy a board that suits your needs - it could be expensive, yes, but if you compare the price for parts, the know-how needed to make it, the efforts to route the board and to interface all components together and the manufacturing equipment that is needed to make it ... then the price of the ready board is actually good.
I was working with DSP boards combining fast ADC, DSP processor and FPGA custom logic, VGA port for interfacing - all interfaced together ... This is I think a good example of complex development platform. Making this at home really make no sense.