Get a minimum 3 mpixels and preferably 4-5. A 5mp has gone down to about $1200 US dollars. That will give you excellent pictures. They are within the price range that you quoted.
Several makes use the same electronics. Essential is ease in handling, to YOUR feel. Nikon, Olympus, Sony, Fuji Leica, Kodak, Minolta, Canon all good. I just got a catalogue which lists a Sony 5 mp with a 5x Carl Zeiss zoom for $1800 in Canadian dollars, within the range you quote. Another I have seen has a Leica summicron lens, I think a Fuji, in the same range. A Nikon 5mp lists at $1600 Canadian dollars.
For small size, the Pentax Optio, Canon S40 and Olympus D40 offer 4mp for $1100 Canadian, but these lack some of the features of the larger models.
Sony offers one with a rewritable cd and Zeiss lenses for $1800 Can., but just 3.3 mp (good detail in 8x10 prints).
Confession- I still prefer my 35 reflex with interchangable lenses if i am taking a lot of shots.