At that price range for the radio, you will be limiting yourself to a mid-price portable (or maybe - just maybe - an older HF ham radio, many of which have a general coverage rx built in). I'm not up on the SDR market - let's see if someone jumps in on that.
In any case, we have a wiki category that links LOTS of places for reviews. Do your homework first!
Category:Receiver Reviews - The RadioReference Wiki
If you're using a portable, then active loops are a good choice. Their signal levels aren't as prone to overload the front end of a radio, and the better ones have a gain control. The Sony AN-LP1 is widely considered to be the king of the hill - if you find one in good shape, grab it - it's been out of production for awhile.
Anyway this article has a few such loops that are HF capable (most are MW only), and would at least give you some ideas of what you are looking for...
Loops - The RadioReference Wiki
If you want to put some wire up, at least with a portable, don't put up more than 30-40 foot or so, or you will risk overloading, particularly at night when the lower bands really open up now. Watch out for static discharges - if you clip a wire antenna to a whip, static can blow the front end amp pretty easily. There's a simple schematic about 1/2 way down this page for something you can build to help alleviate this problem...
WD8DAS Spitfire Page
Finally we have several sites linked with online tunable HF radios - even some SDRs!
Live Tunable Receivers - The RadioReference Wiki