Well a laptop is better for portability, and will run Mir fine even with an integrated graphics chip. Desktop is better, and cheaper performance most of the time, and integrated graphics again would run Mir perfectly. Depending on the other games you want to use, you could probably get a cheap mid range graphics card in any system and it'd run fine. Check something like...
Computer Planet, Novatech, CCLOnline, most websites now do prebuilt desktops, Novatech are one of my favourites and found Computer Planet today whilst on the search for a shuttle.