7750 BE vs 5050e: the 5050e is basically a 5000+ with lower power draw (but identical performance). The 7750 BE matches a 6000+ performance-wise, so that's what AMD think of the relative performance - 20% better! On the other hand, fully loaded a 7750 BE will pull 95W, whereas a 5050e will only pull 45W - and that's a massive difference on an HTPC-type platform. So, if your gaming will be very occasional and you'll mostly be watching DVDs / BDs, get the 5050e to save the electricity bill
a lot - if you plan to game quite a bit, then it's probably worth getting the 7750.
The
size of the TV won't matter half as much as the resolution. a 37" TV could just as easily have a native resolution of 1366x768 as 1920x1080! The former will probably be rated as 720p compatible, the latter as 1080p. If it *just* says HD compatible, it's probably 720p but you're better off checking!
The integrated graphics on a 780G board will easily cope with DVD / BD playback at any resolution, but will struggle with gaming at anything higher than 720p. If your TV is an *OLD* HD TV then it's probably only 720p anyway, but you should probably check that. Even if your TV has a higher resolution, you can always set your games to play at a lower resolution - it won't look *quite* as good but you're never going to get ultra-quality in games from integrated graphics anyway - if you could ATI and NVidia wouldn't be able to charge £100s for the latest graphics cards, would they