I.ll asume that you have a stock Slimline running a 220w psu and that you have 4gb ram, duo or quad proceesors and 500g HDD. The main thing you will need to look for is LOW PROFILE otherwise the card will not fit in the confined space of the slimeline. #2 LOW POWER. with these things in mind your options are limited. Here are some choices~
1. ATI 4350 about 40-50 dollars pretty common in HTPC very low power NOT a gaming card
2. ATI 4550 55 bucks better HD Light gaming low res.
3. Ge force 220gt 60 bucks better res
the 2 best cards That could find are:
4. Sapphire HD 4650 65 bucks runs cool fairly quiet. great HD encoding OK gaming only needs 30w power
5. Galaxy 9600gt Low profile Low Power 109.00 runs warmer best for gaming good HD needs 60w power. you may need to upgrade your psu for this card to 270w.
I have heard that possibly a 9800gt may fit in some slimlines but it is a psu upgrade for sure to at least 350w
Remember Low Profile and Low Power hope this helps