If you see black bars at the bottom and top then your DVD's anamorphic.
Generally film DVD's are anamorphic, and recent TV-Series DVD's are 16:9 widescreen. But I do have a US R1 Monster Inc which is 4:3 (price was cheap, and I didn't read the advert properly.........

).
If you have any favourite films, check the back of the cover 2.35:1 is anamorphic (black bars top/bottom), 1.78:1 (can be different, 1.75,1.88 etc) is 16:9 widescreen, 1.33:1 is 4:3 non-widescreen.
I prefer to watch everything in its orginial format, whether that be 1.78:1 for TV Series (or 1.33:1 for classics), or Films at 2.35:1. I think you can even get wider aspect ratio's............I'm not that much of an expert on DVD's.
Just noticed that my "A bug's Life" DVD is a flipper 4:3 (1.33:1) on one side, and 2.35:1 (anamorphic) on the other.
Some Maths............
15" 4:3 Ratio TV
TV Diagonal 15"
TV Width 12"
TV Height 9"
2.35 Height 5.1"
16:9 Height 6.75"
15" 16:9 Ratio TV
TV Diagonal 15"
TV Width 13.07"
TV Height 7.35"
2.35 Height 5.56"
16:9 Height 7.35"
The 16:9 15" TV is basically 1/2" higher and 1" wider than the 15" 4:3 Ratio TV when watching widescreen images. But personally I would go for 17" widescreen.....worth saving a few more weeks, and you could get one in the Christmas / New Years Sales. Widescreen is more future proof, quite a bit of TV is now broadcast in 16:9 thesedays.