What model Mac Mini do you have?
If it's the A1176, you can perform the CPU upgrade. However, this model only has 802.11b/g, so 802.11n would not be possible (unless you also buy an upgrade kit for the wireless card). From my experience though, b/g radio is fine for HD video. If you do have the A1176, the biggest limitation for HD video will be the video card. I used to have an A1176 upgraded to 2.0 ghz and 2 GB ram. I also added an SSD. With this config, 720p video was fine, 1080p it got choppy. I would watch out for deals on an SSD - this will be the biggest performance increase. My machine with these upgrades ran perfectly for anything not largely dependent on the video card. Booted in 15 minutes, web browser, finder, etc respond instantly.
FYI I put Lion on my upgraded machine, and it ran perfectly, but you have do some hacking to allow it to boot. It's fairly simple, see this thread -
https://forums.macrumors.com/threads/1107457/
If your model is the A1283 or later, as far as I know the CPU is soldered on the logic board, so you couldn't upgrade it beyond the stock config.
I'm assuming though you have the A1176 based on the CPUs you referenced.
See iFixit for more details on what can be upgraded and wikipedia has a good table that shows the details of each model.