I have used a portable cd player with an advertised 120 seconds of memory (to handle skipping problems), but that was not enough. After a while when I was jogging, it stopped working.
Earlier, before it broke, I had a Panasonic that did not have this memory problem caused by skipping. It just kept working
I am out on rough groud for 90 minutes or so, and there is apparently a lot of shock to the CD player that causes the skipping.

A: actually you need a shock holder that holds cd players and lets them move and not skip because the antiskip feature actually causes skipping after a while

I have used a portable cd player with an advertised 120 seconds of memory which was not enough. Earlier, before it broke I had a Panasonic that didn't have this memory problem at all. I am out on rough ground for 90 minutes or so and there is apparently a lot of shock to the portable cd player.

A: Any ipod with FLASH memory, the ones with the hard drives skip like CRAZY...

Flash memory iPods include:

Ipod shuffle (very convenient)
Ipod nano (thin, can watch video)
Ipod touch (Inconvenient, large)

You can also go after the creative zen V plus, it comes in 1GB, 2GB, 4GB & 8GB capacities.

I want to get a portable cd player (I already have an mp3 player, but I want something to just throw a cd in if I feel like it) but I don't know if I should go for a regular one, one with a tuner, one with mp3 functions, or one with both a tuner and mp3 functions. Also, I'm looking at a few Sony models and a couple of Panasonic models at the moment, is one brand better than the other? Thanks.

A: Nowadays, I would definitely buy something capable of playing MP3 CDs. Tuner is a more personal decision. I would take it.
Both Sony and Panasonic are top brands. I don't think there will be much of a difference for a portable CD player.