You don't have to extend your budget to $250. that's some pretty random advice right there. It wouldn't make any sense for a, correct me if I'm wrong, audio-beginner to go way over his budget and buy an expensive in-ear monitor and stick it into his smartphone. Be sensible.
For $150 you can get some really nice sound quality and a great first step into portable audio. A Sansa Clip+ (or Sansa Fuze) won't cost you more than $50, has great sound quality and is Rockboxable (great third party firmware with excellent eq support) which means you can spend the remaining $100 on a pair of nice in-ears. There are a lot of wonderful options in that price range.
Check out this great thread and see which one fits your budget.
Just to get you started, here are some of the most popular in-ears right now. The prices are my estimates though. Check online for current pricing.
- Brainwavz M2 $50
- Fischer Audio Eterna $65
- Etymotic MC5 $70
- Head Direct RE0 $80
- Hippo VB $80
- Panasonic HJE900 $110
- Radius DDM $150
- Fischer Audio DBA-02 $150
- Sennheiser IE8 $350
- Earsonics SM3 $350
- JH13/JH16 $1200/$1500
- JH-3A $a gazillion bucks
There are ofcourse a lot more options in your budget. $150 is a good way to start off with.