HD players are not very prone to skipping unless you want to use them while running or engaging in some other sort of exercise. I've never had a problem with ordinary walking. Flash players have smaller capacities, but that is improving as Flash prices come down.
The iPods are generally as good as any players, but their biggest advantage is iTunes. Firstly the software is as good as anything out there - and quite a bit better than some. That's fairly important if you are planning to rip music from CDs. The other half is the iTunes store. While the AAC format preferred by Apple works on some other players, only iPods have Apple's DRM software. Nothing else can play music bought from iTunes (although iPods can play unprotected MP3 or AAC files quite happily).
For other players I'd suggest looking for reviews of individual models. I've heard good things about some iRiver and Creative models but not all are equally good.