My son has a pair of the Presonus Eris E8 XTs and they are excellent (XT are the more recent, better model of the Eris line). Great clarity and depth of field in the sound, smooth highs, and more—and more controlled—low end than many monitors in the price range.
To be clear, I am aware that they are over your price range. But I mention them for several reasons. First, they have several models with smaller low end drivers that are in your price range (
https://www.guitarcenter.com/Presonus/Eris-E5-XT-High-Definition-2-Way-525-Nearfield-Studio-Monitor.gc?rNtt=presonus eris&index=4) and that have the same design to them, so might be equally awesome, but I haven’t used myself, so can’t recommend personally. Second, they are close enough to your price range that you might be able to find some used E8 XTs in your price range. Third, Presonus also has a subwoofer in the line that you could add later if you find it useful if you buy the 5.5 inch ones. And finally, they carry them at Guitar Center, which has a generous return policy. Monitors are a pretty personal thing, and having that would be helpful.
Hope this is useful to you!
Quick edit: the Eris are powered, and have several tone shaping switches and pots so you can adjust to your room and frequency response preferences. Nice eq points, and are really effective.