Most hardware devices work out of the box on Linux based systems. The only potential issues are with the performance of ATI video cards and some wifi chipsets such as realtek wifi devices. By what I have found online that computer should be using an Nvidia video card and a ath9k wifi card. the Nvidia cards perform really well with the nvidia driver installed which is usually really easy to do and the ath9k drivers are built into the kernel. I don't see any reason for you to have issues.

As for the question about which version is best for online gaming, if you are a serious gamer you want to pick a lightweight distro that will leave plenty of resources for the game, so something like lubuntu or xubuntu would be good options.