I'm writing this with the intention of helping people choose a camera, but for a moment I digress...
Recently Vija's been helping clean out her grandparent's place. I already have five cameras and I don't really own any of the new ones but none the less I get to use them for the moment. I've been rocking the 35mm Zeiss Iknota from 1949 recently. Here's a photo I recently took and developed with some really expired Kodak B&W 400TX.
From left to right: Mamiya 645 medium format film camera, Linhof Technika V 4x5 film view camera, HD Hero helmet camera, Zeiss Ikon Ikonta 522/24 35mm film camera, Hasselblad EL medium format film camera, Zeiss Ikon Contarex Electronic 35mm film camera, Holga medium format film camera, Diana+ medium format film camera - photo taken with my Canon T1i DSLR.
Anyways, here's the thing, point and shoot cameras are alright for 90% of people and that's fine. Their quality has reached the point where their resolution actually surpasses 35mm film. The point, however, is that no matter what you choose there is always a trade off.
The most important considerations in choosing a camera are:
#1 - the best camera is the camera you have with you.
#2 - the bigger the camera the less likely you are to carry it.
#3 - digital is the way to go. I love and will continue to use film but it's dead except for very niche uses.
The combination of these things is the reason why camera phones are so popular. So that leaves most people with a point and shoot, a few people with a DSLR (digital - single lens reflex - it means that what you see through the lens when you have your eye to the viewfinder) or bigger, and a few confused people who don't like either choice of the $200-300 point and shoot or the $500-800 DSLR.
I'm not going to go into point and shoots - plus, camera phones are making those obsolete fairly quickly.
The middle ground is something like a Canon G series camera - the G11 being the latest. The advantage of these cameras is that they aren't much bigger than a regular point and shoot, they are closer to the price of a point and shoot at just over $400, they have much better image quality, you can control the camera manually, and their ability to shoot in low light is actually better than most DSLRs. I know a few pro photographers that use these and I highly recommend them. They're gaining something of a cult following.
DSLRs are large because they have bigger sensors, bigger batteries, and they have a mirror. By definition one sees through the lens in a SLR unlike a rangefinder where the viewfinder and the lens are separate. Thus, it requires a moving mirror which adds bulk. If you're going to get a DSLR I recommend a Nikon or Canon. I prefer the Canon but to be honest they're nearly the same. I think the Canon rebel series gives more bang for the buck but it's up to you. Get the lens kit and if you want to purchase another lens I recommend the 50mm f1.4 lens. When purchasing a DSLR remember that there's a 1.6 crop factor. This means that any lens you put on the camera will become 1.6x greater in focal length, so all your lenses zoom in more. The 50mm becomes an 80mm - good if you're into zoom/telephoto and bad if you're like me and love wide angle lenses (Tokina and Sigma make 11-16 and 10-20mm lenses specially for these cameras).
The reason I don't advise a DSLR to most people is that the camera ends up laying around because they are too bulky to lug around. Most people also don't use the ability to change lenses which is probably the best reason to get a SLR. Lenses are what make great photos (among other factors). Also, people rarely learn how to use them in manual mode. If you don't change lenses and leave it in manual mode then why not just get a point and shoot? "The image quality is better..." If you want the best image quality a SLR is unsurpassed - true, but who buys an automatic sports car?
The best place to buy camera equipment is a store called B&H in NYC. They more or less have a monopoly on selling camera stuff because they run a great business. If Google owned a camera store this would be it. Also, eBay is a great source for cameras. There are tons on there that are barely used and sold for far below what people paid for them. You can usually save 30-40% by buying the next to latest model of a camera that's barely a year old.