I have a few shortwave radios. One that is well within your budget, and that has much better sound quality than many small/cheap radios, is the Radiwow/Sihuadon R108. It runs for about $60 on Amazon and other places.
https://www.amazon.com/dp/B08XVVCP9LI often bring it with me when I travel for work, since it is so small and sounds so good. It comes with a wire with a connector to use as an antenna, but the jack on my radio doesn't really work. So I usually use a wire antenna that clips onto the antenna and then run it to a curtain rod; something like this:
https://www.amazon.com/Sangean-ANT-60-Short-Wave-Antenna/dp/B000023VW2The main thing it is missing is single-sideband. The one annoying thing is that when you run the scan feature when using headphones you get a loud 'pop' when it lands on a station. Since the pop is not dependent on audio volume, I use an external attenuator (resistor-divider in a nice case) before the headphone then turn up the volume; now the pop us a subtle thing. My much more expensive Eton Elite Field radio has the same problem...
If you want single-sideband, which is what a lot of the amateurs (and some pirate stations) use, then the cheapest model I know about (but have not used) is the Tecsun PL330
https://www.amazon.com/Tecsun-Digital-PL330-Worldband-Receiver/dp/B0921HN6QMIt does not come with a wire antenna, so would need one.
I see that you are in the US. Note that most of the domestic shortwave stations have schedules that are dominated by religious programming, and of course you will find conspiracy theorists that I won't name. I mostly enjoy listening to stations from other continents. There are websites to help you figure out what you are listening to (can look up by frequency/time/language), which is 'easy' when using a digital radio since you know the frequency precisely. To be honest, for me at least half of the fun is learning how far away I am from the transmitter. For content, I usually listen to FM, which is why I mentioned the sound quality on the first unit. Some of the shortwave radios can sound pretty tinny; I bought (then returned) an Eton Elite Executive which was beautiful through headphones, but the sound quality through the speaker was what I would expect from a $5 throw-away toy.
You can find reviews of both of these (as well as 100s of other radios) on Todderbert's youtube channel. I have no connection to Todderbert, but he will go through various features. He mostly talks about AM and FM performance, but does some shortwave as well.
Jason
EDIT: I agree with themadhippy.