Your computer specs say that there are both PCI and PCIe ports on your motherboard so unless they are both populated by other hardware you should probably select a PCIe adapter. To be sure of this you should probably open up the case and check out whats inside and which, if any, ports are free.
A PCIe port is faster than a PCI so it will support better speeds through wireless.
Secondly, check out your wireless router to see what speeds it supports. Have alook at the manual, if you don't already know what the wireless speeds may be. If the router is G class it supports up to 54Mbps and if it is N class it should be 150Mbps or greater. Most Wireless adapters are backwards compatible so if you choose an N class adapter it should work fine with a G class router, but your speed will only be as fast as the adapter can support.
On the other hand a USB adapter will probably do just as fine a job as PCI or PCIe and be much easier to install.
As for your selection, if you are not a really "hard core" user don't be too worried, pick one out that suits your budget and always be sure that there is decent warranty on the product. If possible buy from a shop that will accept a return if you are not satisfied, that way you will have a back up option.