I'm a big fan of ultra-portable laptops, as I love having lightweight laptops that are easy to carry around. Keep in mind, I'm not saying netbooks, as I wouldn't buy one of those for $75.
Before buying from a brick and mortar store, look online at places like newegg.com because you can usually find things a little cheaper there. I recommend a minimum of 3 GB of RAM (and I personally never settle for anything less than 4 GB) and, depending upon how much music you have, a 320 GB or 500 GB hard drive will suit you just fine.
As an example, all of these laptops weigh under 5 pounds, and have at least 3 GB of RAM and 320 GB of hard drive space.
http://www.newegg.com/Product/Product.aspx?Item=N82E16834214398
http://www.newegg.com/Product/Product.aspx?Item=N82E16834157838
http://www.newegg.com/Product/Product.aspx?Item=N82E16834214401
http://www.newegg.com/Product/Product.aspx?Item=N82E16834157881
http://www.newegg.com/Product/Product.aspx?Item=N82E16834157883
Some are lighter, some have better processors, some have more memory, but all are under $600 before tax. You can rate processors and video cards here:
http://www.cpubenchmark.net/
Also, just out of curiosity, when you say your current laptops are about to give out, how do you mean?
That's probably the worst idea ever. No, seriously, an absolutely awful idea. To the point where giving out advice is probably something you should look to avoid in the future.