Hi calranthe, for a start, these benchmark lists should give you a fairly good idea about which graphics card (GPU) to get: click here, click here & click here.
Most laptops these days have fairly good basic specs - dual-core CPU, 4Gb RAM & large hard drives. So choose a few laptops with GPUs from the above links that will play your games (or some of them) on medium settings at the very least. As a gamer, the GPU ideally needs to be the best you can afford / fit in your budget. The rest of the spec will be good enough to cope with the games & just about everything else.
Post the links of some laptops that you think will be suitable. Then we'll take a closer look & let you know either way. G