You're going to have a lot of fun with the 320; lots of software for it, some of it free (by far, I think you'll find Shortwave Log to be one of the most powerful, and it's free) - if you haven't joined the RX320 Yahoo group yet, I'd encourage you to do so....
http://groups.yahoo.com/group/RX320/
Tons of links and other articles in their 'links' section.
Antennas are better addressed in that forum, so I'll keep my comments general with a few links thrown in - by the way anything I mention here will work just fine with that old Hallicrafters as well as the 320 (I started off renovating an old SX110 that took a near-lightning strike)...
Living in an apartment, you need to avoid antennas that will simply increase your noise level - just throwing a hunk of wire on the ground will certainly pick up signal, but your neighbor's light dimmer, TV, fishtank heater and darn near anything else that's a potential noise source. Using a coax feed, plus a transformer or a good sized loop are the tickets here.
Before I start, if you don't know how to solder, it's time to learn. It's a skill that will carry you well in this hobby. Make friends with a ham - get in touch with CARMA (seem like a good bunch over there). I understand they even have local meetings.
Here are just a few suggestions for antennas - there are so many more, I'd do some research on the antennas wiki on this site...
A.
The Carpet Loop ; I've tried a smaller version of this, and the results are interesting.
B. The Attic loop as shown on the main page of the
Shortwave SWL Antenna Yahoo group. Using thin clear wire will keep the visibility down. This is a good choice if you have access to a crawlspace or attic
C. The PAR EF-SWL antenna. If the wire is too think and visible, you could substitute a thin speaker wire, and hide the transformer behind a desk. The coax can easily be pig-tailed for the old Hallicrafters. It's very widely available from many distributors.
D. Normally, I'm loathe to recommend active antennas, due to the fact that many amplify noise as much as signal, and in an urban environment that's something you don't need. But if you'd like to try your hand at a kit, I understand the
North County Active Antenna works pretty well.
There - that oughta get the brain cookin' 73s Mike