There are several mp3 related applications available.

Players

Winplay3 2.0 this was the first windows mp3 player out. With Winplay you can change the configuration to work with a 486. It will read a playlist which is necessary if you want to listen to a lot of mp3s at once. Winplays look mimics a front of a cd player. The main problem with it is that the rewind and fast forward button were actually for use with a playlist to skip to the next track. 

Playlist Editors

fliptech Shuffleplay 2.00 is a playlist editor that will tell winplay to play a list of songs also has a random play feature. It will minimize itself to the win95 toolbar and will also minimize Winplay to the toolbar. 


XMM is another mp3 file manager, you can edit the tags of mp3s, create playlists and play songs,  a special area for lyrics, this is one of the best examples of mp3 manageming applications I have seen so far, it is a little different from shuffleplay but either will work well.

fliptech Visual Encoder 1.31 this is basically a windows95 front end shell for the L3V260D1 Dos encoder. It is simple to use and and easy to set up.

MP3 Playlist Maker is another playlist maker it claims to be able to hande complex directory structures.

Recommendations
I recommend Winplay 2.0 and Shuffleplay, and  XMM because they work well together, and will work with a 486. They are straightforward and simple to use, you don't have to even look at the help file to get started.