With respect, most folk will tell you to get what they got, because you'll love any modern camera and the pictures you take. Don't do what I do and get bogged down in details, it ends up spoiling your photography and giving you buyer's remorse with whatever you get.
Take in as much info as you can, but before your head starts to hurt just buy something and start taking photos.
As for compact vs. SLR, here are my thoughts, I'll leave behind the earlier important points about size, cost etc.
Picture quality: 10mp compact does not equal 10mp SLR. Smaller pixels mean more noise and some cameras overcompensate this. As Red says 5mp is adequate in either format, but there is this difference. This, however, is an academic difference until you blow your pictures up greater than A4 size.
Control: This is the big difference. If you understand f-stops and how aperture/shutter speed effects your photos and want to control this you need an SLR, or one of very few compacts.
Depth-of-field: Real photo-geekery here. But depth of field is deeper on a compact than and SLR (I can explain why but it will be longwinded, I warn you). This means that under given light conditions, you can get more front-to-back in focus for your landscapes and macros, but for arty portrait type shots, you can't blur the background as nicely on a compact.
Build-quality: SLRs probably more robust for use out and about, but need to be because they're so big. Look for metal-bodied compacts where the lens retracts fully.
Finally: To follow from my first point, I've used a Nikon D70s for 2 years and film SLRs for 10 before that, They're great but this week I'm selling it all to buy a Ricoh Caplio GX100. It's a compact that gives you all of the control you get in an SLR, I prefer wide to telephoto so am going to live without distant wildlife shots (of which I get very few good ones) and focus on the details and landscapes that I get more success with. I am going to use photoshop to compensate for the other artistic shortcomings I mentioned above. The emphasis being on lightening my load. Since I almost always carry my camera. I will be walking around 3kg lighter!