According to this Windows 7 Compatibility D-Link D-Link DGL-4500 Xtreme N Gaming Wireless Router
the D-Link is compatible with both 32bit and 64bit Windows 7 versions with no additional action required (out of box). However that is a draft N router and to get the full benefit of its' performance, your devices would have to be N type devices, but it is backward compatible with a b and g wireless so that's not a real problem.
According to this Windows 7 Compatibility Linksys Linksys BroadBand w/SpeedBooster 72Mbps 802.11g 4Port Wireless Router
the Linksys is compatible with 32 bit Windows 7 after a firmware upgrade and there is no information regarding Windows 7 64bit. I have personally used this particular router with Windows 7 ultimate 64 bit and while it worked, I was not at all pleased with the actual wireless performance even when my wireless device was very close to the router. (Your mileage may vary)
As for the ISP upgrade in service, I'm all for the latest and greatest, biggest and badest...but it's usually about your personal budget. Streaming video would be all about download and I would think that 7megs would be more than sufficient, would 11 megs be better, well if you're having problems with buffering now, then I would think yes, but I would wonder more about the source of the video and how busy their servers are. Gaming is bi-directional up and down and while the upgrade would double your upload performance don't expect it to work miracles, there are a ton of people out there with cable, fios and uverse that have some incredible up and down speeds. So to summarize I guess I would say, if you can afford it, go for it. Just don't end up doubling your monthly fees for what is not actually going to amount to doubling your internet performance.