While there are many benefits of DSLRs for us hobbyists / professionals, to an everyday user they are often a burnen which ends up collecting dust and then re-sold after the value depreciation.
Fo every-day photos I doubt very much one needs more than a compact (i.e. Canon Powershot S100 which is a very capable little camera which even pro's use for travel / scouting).
If you don't want the weight but want the flexibility of depth of field / focal lengths than as others mentioned, mirrorless systems may be an option as well (Olympus PEN, Panasonic GF2, Nikon 1, etc)
However, if you are serious about learning photography and using it for a wide array of applications then a more serious kit may be in order. However, I would first look at the budget and purpose and then make a recommendation based on that. Often times, money is better spent on quality accessories (such as Tripod / head, glass, filters, lights) than on a camera body. DSLR bodies change all the time, but a solid investment in glass / tripod will last for a long long time. It all depends on the need.
I would agree with 80% of what climber is saying. However, the Op mentioned that he will be taking alot of indoor pics which means that low light ability is an important consideration. A DSLR will generally be less noisy and allow the user to select a higher ISO so as to avoid using flash while handholding.
My personal bias - let me first say I really like the Canon S100, however, for many instances where a P&S form factor is appreciated I think something like an Apple iPhone will do. Therefore, I don't see the need for a p&s if one has a nice smart cameraphone.
Depth of field - control over this is very important even to beginner photographers, and the OP wanted to grow into his camera. Hence, if he doesn't mind the bigger bulk, then a DSLR is the way to go. As I said, the Canon 5DMkII will be dropping in price and this is a great camera (full frame is in my opinion the way forward - I am old school film guy and the crop sensors just don't do it for me). The camera is not important used to be the mantra in the film days, but with today's digi cams, the camera is becoming increasingly more important.
But then the OP never stated his budget, so whilst a 5DII is value to me, it may be too much camera for him price wise.
However, indoors the difference is huge - the dSLR with optical image stabilization, fast lens and better noise control at higher ISO creates stunning shots whereas the smaller ones are unusable without flash. Fast lens and dSLR is definitely the way to go if you want to shoot indoors without flash.
Thanks guys. Just wanted to give you all an update that I got a Canon 600D. I appreciate all your help!
If you haven't done so already, I would highly recommend that you purchase a 50mm f1.8 lens (dirt cheap and fast)....although a bit long for a cropped sensor. Not sure if Canon has a resonably priced "normal" focal lens alternative (i.e. 28mm f1.8m, etc)...if not you may want to consider a third party...such as Sigma 30mm f1.4.
Thanks everyone I got 600D with the 18-135mm lens. Btw... everyone says OP here. I figured it was me you guys were talking about... but what does OP actually mean?
After I get the time to read the manual fully, I'd like to participate in some photography groups on here. If you guys are in any of those, I'd like to join some time