I run a combined MythTV front&back-end on my F10 box using the packaged software from RPM Fusion (http://rpmfusion.org/
). Avoid multiple repositories if at all possible!
The MythTV wiki site (http://www.mythtv.org/wiki/Main_Page
) covers Fedora installation. The documentation is a little out-of-date but is a good starting point. You should find answers to any MythTV-specific issues there too.
I don't have any experience with on-board graphics with MythTV, but if you can play MPEG2 files full-screen OK using MPlayer etc. you should be fine.
Check the boot-time kernel output using `dmesg` and look for names or identifiers for your TV card, or the output from `lshw` or `lspci`. Check the LinuxTV web site (http://www.linuxtv.org/wiki/index.php/Main_Page
) for card-specific support etc. The F10 kernel modules are fairly up-to-date.
Hope this gets you started!