If all you want is a media center, you're probably better off going with MythTV, either added to a linux distro or by installing a MythTV specific distro such as Mythbuntu.
As for how to control LinuxMCE via remote, in general if the device works via lirc it should be able to be made to work with LinuxMCE. It's also possible to use lots of other things as a remote such as various air mice, nokia tablets, blutooth adapters + cell phone, RF gyro remotes, etc. The real question is what is plug and play and what is not. The Fiire Chief remote is plug and play, as is USBUIRT + a MS MCE remote, and I believe the Gyration Go Mouse. Other variations will likely work out of the box, but you have to add them manually (not plug and play, but the config is there). At the other end are devices that can be made to work, but take a bit of hacking such as USBUIRT (plug and play receiver/transmitter) or a LIRC receiver + unsupported remotes. If at all possible, stick with a plug and play device. Be prepared for people to tell you if you are using LinuxMCE and USBUIRT there is no reason not to have LinuxMCE control your TV/hi fi.
I don't really know much about bluetooth support or if anything other than certain phones are supported. You'll likely have to search here or lirc sites to see if your specific hardware will work.
You'll probably need to search here, or more likely the lirc sites, to see if your specific hardware is supported.
