Morning tickmike and unkyUb.
Tickmike, as unkyUb has said, there is such a huge variety of cameras on the market from cheapo point-and-shoots to expensive and complex dslrs and "bridge" ones that it is difficult to make any sort of recommendation without a wee bitty further information from yourself.
How experienced a photographer are you, do you want a camera that will do everything for you, or do you want to control all aspects of the process, or something in between.
What is your budget
What do you want to do with the resulting pics, this has a strong bearing on the amount of megapixels you should buy.
If you are going to put the pics on websites for all the family to see, you dont need a huge dollop of Mgps, three would be adequate............if you are going to print the pics either at home or at the likes of Boots, what size of prints. If you only want say 6x4, then three Mgps is enough............if you want A4, then go for 6Mgps or more.
An important consideration is the size of your hands, very small or very large cameras can be uncomfortable or cumbersome.............go to the shop and try a few for size, checking that you can get easily to all the buttons and controls.
UnkyUb has made mention of some camera makers and brands, and none of these will disappoint...........the Canon that he has linked to is a very nice little machine and is indeed a great "starter" model, not too expensive and fairly comfy in the hand.................and his point about having a viewfinder as well as the LCD screen is very important, a viewfinder is better in all respects than trying to compose/snap using only the screen.
Let us have a litlle more idea of your needs, and we will roll some more direct options around.