The market is flooded with many players that are cheap & look great, but may last only a while. Don't go by looks alone. Best to play more for a good brand rather than risk losing it all on something cheap.
Display. Most Mp3 players have small screens. But choosing one with a big enough screen that displays JPEG & BMP digital files can be useful for viewing digital images conveniently.Advanced features. Some models are capable of creating play list. Look for smart play lists, song-rating methods, automatic volume control, Wi-fi, blue-tooth, audio recorder, FM radio.
Storage capacity. Get the most space you can afford. If you are going to make this supplement your home entertainment system, then space better be large. In general, those with hard disk offer more space than those with flash memory. But flash memory won't suffer a mechanical breakdown or skip musical beats when jerked about or played while jogging. Also look for a slot/plug-in for SD & flash cards.
Battery life. Check the manual to see hoe long dry cells will last. it may be wise to buy a player that uses rechargeable batteries. Check whether the manufacturer has a guarantee plan that replaces inbuilt-rechargeable batteries that may fail.
Headphones and sound. Finally its all in the sound. Don't buy any music system without really listening to it. Get a player with a standard 3.5-mm head hone jack, and not an "only ours" proprietary jack. Switching to better headphones, too, can make all the difference.
Dock. Make sure a compatible dock for the player is available. Invaluable especially if you're rigging it to a home system, because the dock will keep the player charged.