You can make this as complicated or simple as you like....
... and as with anything - the more time and effort you put into it the more you will get out. On the most basic level - I say you can get by on something as little as 3 or 4 megapixel for most applications so a basic digicam should serve well. And with a 4, 3 or even 2 megapixel cameras your memory cards will go much farther. 3 megapixels is enough for 8x10 images. On the other hand if you get sucked into the more mega-pixels is better thinking then your memory cards will have to be bigger - and your storage limits MIGHT be noticed on your computer HD and CDs or DVDs.
A few hints and pointers up front. If you post process your images (IE, sharpen, rebalance color, crop, fix red eye, etc.) then every time you save an image it gets compressed and will lose a little of it's perfection. Always save to an alternate file name so you have an original image that has NOT been rewritten as a JPEG.
Next - when you store your images to CD or DVDs - bear in mind that this sort of storage is not expected to last much beyond 10 years. If you want it saved securely then you need an external hard drive. I have CDs that have delaminated at 5 years making part of the CD unreadable. I have since transferred my entire photo archeive to an external hard drive and I store that in a fireproof safe.
I print to Costco online for local pickup (4x6= $0.15 up to 12x18 for $2.99), and use an online subscription service too. Plus I have tried printing the bound 4 color process books and recently started using propixexpress for prints on Kodak Endura paper pressed to canvass and mounted in wood frames. $4.95 in 8x10 and $8.95/9.95 in 10x13! Shipping is a flat $5 regardless of order size for 2nd dfay fedEX.
Also, I would recommend buying from Costco. Just in case you are not satisfied with your digicam purchase Costco has a very liberal return policy - just keep your receipt, packaging and decide if you're satisfied within a few months - or even within the first year. Trying to return after a year will depend on the thickness of your skin - but the reutrn policy has no apparent time limit so long as you have a receipt. Certain items do have a time limit though on returns - such as computers. Computers have an absolute 6 month reuturn limit - pretty outrageous, eh?
Plan on enjoying zero cost image capture; and low cost sharing of images via email. Equipment may become an issue if you get caught up with it. My 1st digicam cost me $900 for a G! the first 2 weeks it was released. And I bought a 1 gig IBM micro drive for $500 at the same time. Now you can get the G1 used on ebay for under $100 and a 4 gig micordrive for under $150. Solid state 1 gig CF cards are to be had for under $50 on promotion too. Currently I have a Canon 10D... a $2000 DSLR which I bought used for $600 on ebay 20 months after it was INTRODUCED! Talk about radical depreciation! So - get something to get started with and if buying the latest and snazziest = be warned that it will be replaced every 18 months with a better model. In 36 months it will be twice replaced and probably available on Ebay for very cheap.
Post processing is also a huge potential issue. You may very well end up spending much more time manipulating and organizing your images then actually shooting them. OR... you might just take your cards to Costco,
Walmart or Target in person and just select 4x6 prints and a storage CD on the spot for the simplistic convenience it offers.
ONE THING>..... do plan on learning how to down load and handle your images. I have cousins and a BIL who cannot off load the images - so they just buy a new memory card when the current card fills up. THat is pretty silly as the storage media is reusable and expected to be reused as such. Oh yeah... do print some of your images in the big size (12x18 or a framed 10x13 at least) every now and then when an image is nice, tac sharp without being under or over exposed.
Here are a couple of fun images I've taken recently....