If you want to directly connect the computers (they need to be max 100mtrs apart) you can use a crossover cable by using Cat 6, 6E or 7 cable and 2 RJ45 plugs. In the cable there are 8 cores and each of the plugs has 8 terminals. You need to connect it in the following way:- 1 on plug end A to 3 on plug end b, 2A to 6B, 3A to 1B and 6A to 2B. This is the cheapest option. Other than that you need to make sure both the PC's have Gigabit capable cards fitted and the buy a gigabit hub or router. You will also need to buy Cat 6, 6E or 7 cables to interconnect the computers to the hub / router. I can't advise on prices as these depend on your local/ inernet supplier of equipment.
With regard to your second question, upgrading to ultimate will cost you more and not necessarily help with your games problem. It depends on what you are trying to achieve. If you are trying to play games over a network you will probably be better with either Pro or Ultimate as these have better networking capabilities. But if it is standalone games that you are having problems with, then you may be able to amke do with your basic version. Try running any install program as an administrator. If this does not work, right click on the installed game and select "Troubleshoot Compatability" from there try the recommended settings or select to run in XP mode.