Can you recommend MP3 players ?

I've used the Sony Mini-disc but quickly got annoyed with the format
changes and software challenges. It was nice at the time, but now there
are so many more options that are better.

I've tried a few different ones. The Rio Cali is great and it's based
on SD memory so there are no skipping issues. The amount of music it
holds is dependent upon the size of the chip, but with a 512Mb chip
(and 256 internal storage), you can store over 150 songs, which is
enough for a pretty long ride.

The Rio Carbon is excellent as well. Stores 5 Gb (1200+ songs) and it's
tiny. Rechargeable battery lasts long enough for an all-day ride. It's
a hard drive, but never had any issues with skipping while riding. If
you're running with it as well, I'd suggest a Cali or similar chip
based memory player.

Just got the Creative Zen Micro - Also a 5 Gb player. Advantages: comes
with built-in FM tuner & voice recorder. But I don't like it as much as
the Carbon due to the shorter battery life on the rechargeable battery
(about 5 hours, though they claim 12). Fortunately comes with a spare
battery and can be changed, unlike most of these types of players. The
one accessory it has that was critical for me was the remote control.
While riding, I wanted to be able to skip songs, change the volume,
etc.

There you go -- I've owned a bunch and use them as follows:
Sony Mini-disc: Retired
Rio Cali: Gym (no skipping when on treadmill, etc)
Rio Carbon: General purpose use, semi-retired but a great player
overall. If it had a remote, it'd be perfect.
Zen Micro: Long rides

No. It's a really bad idea to be wearing headphones while riding.
Listen to music when you arrive safely.