A 128MB MP3 player will just not fit a whole lot of songs, period, but if you want to maximize the number of songs that will fit, you should buy or encode your songs at a lower "bit rate" such as 128kbps (kilobytes per second). The bit rate in this format means the amount of data contained in each second of the song, or how compressed it is. Whether you are using iTunes to purchase, rip or encode your songs to go on your 128MB MP3 player or other software, the most common bit rates are 64kbps, 128kbps, 192kbps and 256kbps.
Check to see what file types your 128MB MP3 player supports. WMA files, for example, are slightly smaller than MP3 files. Apple's AAC files are also slightly smaller than mp3 files, and many perceive them to have better sound quality as well. An older iPod Shuffle, if you can find one, is an example of a 128MB MP3 player that will play AAC files. The difference here is not too large, but will affect the number of songs your mp3 player can hold. WMA files are typically smaller than corresponding AAC files.
The number of songs that will fit on your 128MB MP3 player is affected, more than any other factor, by the type of music you listen to and how long the songs are. There is no reliable way to tell exactly how many songs your player will hold, because classical and jazz pieces tend to be longer than pop and rock songs.
Check the packaging on the back of the 128MB MP3 player you are thinking of buying. Usually there will be a caveat: "Based on 128kbs encoding at a song length of 2 minutes, 30 seconds." Since many songs are longer than this and some of your songs are likely to be encoded at a higher bit rate, always expect to fit fewer songs than the packaging says.
All this technical examination of how many songs may or may not fit on a 128MB mp3 player aside, your real world mp3 player will probably fit 50 or so songs in MP3 format of about 3 minutes in length on average, or 70 songs in WMA or AAC format. That's only a few albums, so unless you don't mind shuffling the music on your player around before you leave the house, consider springing for a player of a higher capacity.
Your best bet if you absolutely have to fit even more songs on your older or cheap 128MB MP3 player is to encode them at the lower 64kbps bit rate. Most songs are encoded at 128kbps or 192kbps, but if you select the songs in iTunes or other digital music software you can compress them even further. Assuming everything else is the same, you will be able to fit twice as many 64kbps songs as 128kbps songs on your MP3 player, though you will start to notice a marked difference in sound quality.