I think Your first question is too general. Some hardware causes issues when working under Linux (mostly because of drivers problems). If I may suggest something, please see Ubuntu certification website. There You can find descriptions of issues (if any) and given workarounds to them. Choose one that is described as least problematic for Ubuntu. That is how I would make a choice if PC is not bought already.
The second thing is, that a lot of hardware producers don't care about (quite large) Linux users community. So if You have chosen some equipment, see what it has inside, and check if producers offer drivers for linux on ther websites or on the CDs/DVDs that come with it. This way You will not only avoid problems with drivers, but also support Linux community by choosing Linux friendly producer.
And personally I would suggest laptop with nVidia VGA card, but that is my personal suggestion.
As for second question: of course You can install Ubuntu
Your processor is 64 bit so You should choose 64bit OS.