I have used my own cable modem and router for years with Comcast. If you are going to do the same, do buy them separately. There is no reason to buy a combo unit. The savings in cost is too small to justify the downsides. And routers have changed much more rapidly than modems over the past few years.
Most ISPs will provide you with a combo unit that they call a gateway for a monthly fee, but they are usually low quality. You will want to make sure to get a docsis 3.0 compliant modem. I have been using a Netgear cable modem for years now with nary an issue.
Lots of good routers out there; both Asus and Linksys have some good stuff. I would go ahead and get one that had wifi, 802.11 a/c and mimo. Even if you are running a cable between your gaming rig and the router you will enjoy having that wifi for your phone, tablet, tv, and what not.
And don't be afraid to use ISP supplied hardware for a little while if money is tight. You can use their stuff while you get well-educated on what hardware you need/want.
Finally, you can also buy just the modem first if you really need the hardwired connection for just your computer, then later get the router.
P.S. Most cable installers will install their cable in the simplest possible manner. In your case, that would be to put it right where you already have service downstairs. Make sure they know where you need to place the cable modem and if at all possible, be there when the installer is there. They may charge extra to run cables.