That's REALLY REALLY tough. Rap and other music don't mix if you listen to rap as it is intended to be heard. I would recommend the event tr-5 as the best speakers I've heard under $300, maybe $500 for professional powered monitors, but the 5.25" woofers won't satisfy your brother 100%. Adding a sub to the event tr-5 would be my choice because you could dial in the bass somewhat to taste, bump it up for rap, turn it down for jazz.
The tr-5's are sweeeeeeeeet imo. You can get them on ebay for under $200 used too. The only problem would be getting a sub. A starter subwoofer would be the dayton 10" powered sub for $125. That's gotten good reviews for tight musical bass. That's the easy way out. If you want something better, the price is going to triple. You can diy your own kick ass subwoofer for about $300, or you can buy the Dayton Titanic sub off of ebay if you're patient for the $250 reserve plus $25 shipping or so. This would be an all powered system. Add preamp and you're ready to ROLL. Or if you use a computer, I guess you don't strictly need a preamp, but I would still use one.
One more tip: The event tr-5 can EASILY be auditioned at your local pro audio center (read GUITAR CENTER.)