Pretty decent radios for not much money ($50-$75)
Degen 1102/Kaito 1102 (same radio)
http://tinyurl.com/ykurhy

The Degen and Kaito would be the minimum I would start with and honestly I
would spend a little more and get the Sony 7600. The Sony 7600 $140 would be
a pretty nice beginner radio.
http://tinyurl.com/ylrxd2

Good Comparison chart of various radios:
http://universal-radio.com/catalog/portable/chartp.html

An very interesting radio is a Ten Tec 320D about $350. A pc/computer
operated radio. A lot of flexibility here. I purchased a used one that was
only a few months old and looked new for $180 a few months back. I normally
wouldn't buy a used radio but this was the exception. These radios are
enclosed in a metal cabinet and pretty much bullet proof. You can download
the software free off of the Ten Tec website to try it out free he
http://tinyurl.com/yeluux The radio can be found he
http://tinyurl.com/ygvhzd There is also other freely available software for
this radio.

Jumping up quite a bit in price is a Grundig Satellit 800 about $420. New
ones are no longer available but units refurbished by Drake (The guys who
made the Drake R8B radio). These are big radios but very easy to use (low
learning curve) and pleasant to listen to.
http://tinyurl.com/yc34hr

One of the hottest things out right now is the Eton E1 which is about $500
but comes with a free $150 Grundig 4000. This E1 is unofficially known as
the Satellit 900.
http://tinyurl.com/ycpxn3

All of these radios can be purchased at:
www.universal-radio.com

The Sat 800, 900 and the Sony 7600 all have what are called sync detectors.
In a nutshell this feature helps to keep an AM broadcast from fading in and
out. It makes a radio much more pleasant to listen to. The one on the Sony
is not too bad but not as good as the one on the Sat 800 and 900. This is a
must have feature if you're going to be listening promarily to AM broadcast
stations. I highly recommend it.

I also recomment ordering the book "Passport to Worldband Radio". The newest
version is available shipped for $23. This has receiver ratings and a wealth
of information about shortwave listening in it.
http://www.passband.com/

If you're really on a budget, you might find someone who will give you last
years "Passport to Worldband Radio". You can also go by Barnes and Noble and
look through the book there for some general ideas.

Shortwave radio is about 40% radio and 60% antenna. These are figures that I
am totally making up but trust me when I tell you that the finest radio
available is nothing without a good antenna. The good news here is that
really good antennas can be made for less than $10. Read as much as you can
about antennas and you will be worlds ahead. Speaking of reading... go here
www.dxzone.com and read untill your heart is content. Pay close attention to
the antenna sections. There are many antennas listed there that can meet
anyones needs.

I hope this gives you a good starting point. If you have any more questions,
feel free to ask. Good luck!