Now let's start with the antenna - the radio is fine, you just need something that is going to be broad banded enough to cover a whole lot of spectrum. If you already have something like a G5RV or Carolina Windom - and/or something that covers all of the HF spectrum without traps, you're set. Alternately loading up a wire with a transmatch is another method - anything you do to make your antenna more broadbanded is going to help. There are a lot of different possibilities here. If you can't put something outside right now, a nice big loop in your attic, fed with a 9:1 transformer is a pretty decent way to start. What is your antenna situation like?
Now let's consider what you want to hear. As a good general rule, in the early evening - say up to about 00 UT or so - the Africans are signing off, but during the winter season you should have a shot at these from local sunset until that time. Euro stations are often heard into the late evening, what few of them are left with English broadcasts anymore (sadly). Latin American stations are still pretty plentiful, and can be heard at most hours of the nite into local morning, depending on their local schedules. I wouldn't at all be surprised if in the 00-01 UT slot, one or two local All India Radio local stations come through if conditions warrant. After about 03-04 UT, the Africans are starting to sign on again, and are possible until their local sunrise. Pacific and Asians stations are most common in our local mornings to local sunrise. A few Asians (primarily All India Radio...) show up from time to time in our late afternoon.
When you look at the NASWA spreadsheet, you're going, I think, to be a bit overwhelmed at the sheer volume of the listings. It's a good idea to try to focus on one aspect of SWBCing, just to get your feet wet. All the things you have learned about sunrise/sunset times, propagation and how to interpret the WWV forecasts - all of that will be put to good use.
There are several mailing lists on Yahoo and other places - one I highly recommend to keep ahead of the schedule changes is the DXLD (DX Listening Digest) Yahoo group run by Glenn Hauser. There are others as well - I belong to the NASWA Yahoo group (membership in NASWA is required for this one), and there's always a plethoria of DX news there. I'm sure others can recommend several others...
The next question is what is it that you'd like to hear? The floor is open....best regards..Mike