> I have a slightly unusual requirement.
Nothing really unusual about this.
> I just have a desktop PC which I use for most of the stuff I do (gaming, video, work, etc.),
> and it's upstairs. From time to time, I'd like to use it downstairs. Is there a wireless solution
> that will let me take control of the PC from downstairs, using the TV (HDMI) as the screen,
> and the TV's speakers to replace my desktop speakers?
What you are asking is how to work remotely from TV room to your personal computer.
You haven't specified any essential details so I need to ask:
What kind of stuff you wish to do remotely?
1) Just access photos on your PC and maybe some media (music, videos streaming)?
For that you need just a simple network media player attached to your TV. Also you need a modest wifi connection between your TV and your PC. Anything that has wifi, can output via HDMI, has a remote and plays media files (photos, audio, video) will do.
2) Maybe do some office work on it?
For that you need a thin client. Probably Android based. That can do VNC or RDP. Also some input devices for that box (USB or wireless keyboard and mouse). And a modest wifi connection.
If you even think about streaming games from your PC you need a powerful wifi connection (like dual band, N standard, *fast* access points). And some device that can stream games from Steam - even small Raspberry Pi box could do that but network performance is essential.
So given above three points you need to have:
- configured wireless or wired network connection between the TV and your PC
- somekind of client device at your TV (Android based set-top box or dongle, something like PCoIP thin client, small Linux client (like RasPI))
- some input devices for your TV - depending on what you want - a remote control for media, a keyboard and mouse for workflow, a gamepad for gaming
But the one thing in common is to have network connection (wireless or wired) between the PC and the TV.