I think that yes, the FZ3 will suit your needs just fine. If you haven't seen these two cameras side by side, I should mention that the FZ3 is *substantially* smaller than the FZ20. It wouldn't make sense to lug all that extra bulk around if you aren't going to use those extra features.
If you do decide to go w/FZ3 - a few days ago the Circuit City web site had them for $359. If you have a store locally, you can order it online and go to the store and pick it up (as long as it is in stock). There is also a rebate of sorts for an extra battery and case. I believe that the rebate is good for cameras purchased by Oct. 31. If the price of these two accessories is taken into account, this would make the overall deal quite a good one, even if you have to pay sales tax. It is also nice to be able to pick it up immediately, and to have a reputable dealer to take it back if it is defective.
I had ordered an FZ15 that turned out to be defective. Since it turned out to be a bigger camera than I expected, I decided to search for a different model, rather than get another FZ15. I almost decided to pull the trigger on a FZ1, but decided to go get the FZ3 since I could get it locally. After using the FZ3 for a few days, I'm glad the FZ15 went belly-up. Although there may come a time that I wish I had manual focus on the 3, I am glad not to have the weight/bulk of the 15. You won't be disappointed with the FZ3, although I do wish they came in black....