I love Priceline and have done very well with it! My hints:
Do your research; know what area(s) you're willing to accept. Use the boards that others have mentioned to see what's "out there" on Priceline. I've found this information to be accurate very often.
Don't use Priceline if your dates are at all wishy-washy; once you're accepted, you've paid for the room whether you use it or not.
Start bidding well in advance; lowball it, expecting to be rejected. Keep bidding every day, increasing your increment slowly, 'til you hit a winner. 1/2 your acceptable price is a good starting point.
2.5 stars or better seems to be fine. At 2.5 you'll get a Courtyard Marriott or a Country Inns & Suites. That's not fancy, but it's a good hotel. 2.5s seem to be most likely to give you a breakfast with your room.
Understand that with Priceline you'll pay NOW for your entire hotel bill. If you reserve through the hotel, you'll pay when you check in.
Once you've hit "buy my hotel now" and you've been accepted, you should call the hotel directly to make sure all is well with your reservation. You can ask for special requests at this point (2 doubles instead of 1 king, near the elevator, etc.) . . . but understand that Priceline promises you one thing only: sleeping space for two adults. The hotel will assign rooms to their "full price customers" first, and if what they have left is a king-side bed, you're not getting your doubles.
Having said that, my special requests have always been granted (but then, I've never asked for anything outrageous). And no hotel has ever treated me like a second-class cusotmer because I've come in with Priceline.
I have noticed that Priceline customers tend to get the less-desirable rooms. For example, I've OFTEN been right next to the elevator -- a noisy location -- and once we were right over the entry-roof of Country Inns & Suites, a location that blocked about 70% of the window. For the savings, we're not displeased.
You're a Priceline customer, not a Marriott or Hilton customer. You will not rack up rewards points for your stay . . . if you get room service or other add-ons, that's kind of a grey area.
Priceline is good for some things, but not all things. If I need just a one-night hotel and I'm not too fussy about just where it's going to be, I'll go straight to Priceline. On the other hand, if I 'specially want to be near a certain activity, or if I want to know that I'm getting breakfast with my hotel, I'll usually just book directly. Also, if it's a difficult time of year, I won't bother with Priceline (for example, I often cannot get a good deal on Priceline for a pre-cruise hotel night -- everyone else is reserving those rooms, and it's hard to get a good deal). I would probably NOT go with Priceline for a one-week family beach vacation -- a time when I would care about having a great ocean-front room, walking distance to this or that.
My own experience with Priceline has been great. I tend to get hotels for about 60% the full price, and I can give up a little control for that!
For your particular needs, I think you're going to have a hard time getting a good deal. You're trying to go to DC at a super-popular time: Right before spring break /cherry blossom time.