Any camera will do and you have several options for easy home printing.
If you do not want to involve a computer than buy a printer which has memory card slots. The ones I know and the one I own is from HP, other brand have them too. They are called Photosmart. Mine does not have a screen but the new ones do, so you can see your photo before printing and even do simple things to it like cropping, selecting print sizes, etc.
Mine is a multi-function model that does photo-copying, scanning and faxing. I was truly impressed the first time I used it. It has an index print function which lets you print a thumbnail of all your photos and then you mark the ones you like, the size you want and how many copies. Put the index print back into the fax part of the all-in-one and, guess what?, it prints the photos you want in the size you want and number of copies! That is certainly the best integration job I have ever seen from ANY technology company.
Some cameras have a direct print function which lets you attach the camera to a printer directly. I have never tried that since it both limits which cameras you can buy and which printers. I would much rather choose a good camera based on photographic merits and a printer based on quality.