This gets away from the antennas topic...but the price range you mention, there are several good portables such as the Tecsun PL 660, and the PL 880, but a good SDR will blow them away any day. Take a look here, and read the first 3 articles (links are always in blue) which discusses the SDR market. There is also a link to our SDR forum where you should go to ask questions...
wiki.radioreference.com
Since those articles were published, a couple of new SDRs have come out within your price range - a Version 3 of the RTL-SDR (the originals did not have HF coverage), and at the high end, the SDRPlay RSPdx. Websites for both, along with reviews of other SDRs, are linked in the accompanying article. Google will come up with reviews (and YouTube videos) on those 2 new ones
Mikie