I've always been a build it myself computer geek. I still look at ads for memory sticks, new CPU's, beefy power supplies, etc. - and get a gleam in my eye.
If you are looking for a basic computer, the all in ones are not bad. If you aren't comfortable cracking open a computer to replace a power supply, video card, add memory, etc. - then I think you would be fine with one. They can actually be a bit more expensive than the type with separate monitor and computer case, but there are some serious good deals going on. Also, have you thought about a laptop?
If I can suggest, do some online shopping. Then call and see if they can meet or beat the deal online. I know that situation happens a lot at a particular company - :whistle