Need recommendations for a 10" TO 13" Flat Screen TV

Can I get some feedback on a small TV for my bathroom?  A 10" flat screen up to 13" screen flat.  I would like to be able to take it with me on my infrequent air flights as well, so would need to use a CD/DVD as well as a TV.  No other options are necessary as I use my main TV to record shows, etc.
Since it will go in my bathroom & the maximum front width allowable is 16".  Also want it to have a brace in the back if possible, but I could always make something in the back to brace a flat screen - I would not put it on it's stand...it would be put on the wall bracket I already have for an old heavy TV (if I take that down I have big holes in my wallpapered wall), so I can't fudge on the width of ithe TV.
I am a picky person & want the best picture as possible in the TV mode (& from the numerous things I've read movies, etc. on most are OK anyway - THERE ARE SO MANY, MANY BRANDS OUT THERE!  Spent hours reading reviews & I haven't read on all the makes yet).  Want an easy remote control to only change channels & turn TV off & on, but is really not necessary as I do have a converter box I could use that has a remote, but the TV must be able to be compatible as I use a Universal Remote (broke one I had).  I absolutely must have the sound loud as I'm hard of hearing.
The TV I have now (tube) comes on for about 2 mins, then no picture for about 1/2 hour, then everything's fine (but I can't take it with me on the airplane either & I don't have a laptop...yet so thought I'd just kill 2 birds with 1 stone so to speak).  But if I have to have one that's not a flat screen to get a really good quality picture & sound that's OK.