Hi Brian,
Since there are pages and pages of great posts so far, you may not even see this. But, if you should run across it, here is my take on your question...
First, I am not a computer "expert", just a moderately knowledgeable user. I bought the Dell Dimension desktop computer I'm typing in 2000, and taught myself how to use it and upgrade various parts with a lot of help from forums like this and various Internet sources. I have no experience with Macs, so can't tell you which platform to go with other than whatever you are comfortable with.
From my experience, and personal speculation, I vote for a Desktop. Here are a few reasons...
1. Reason being that there is just more room to put components in that might a compromise for space like an all-in-one or laptop might have to make. There is also more room for bigger fans and air space for more efficient cooling, and therefore longer component life. As I mentioned, the desktop I'm using is from 2000.
2. Desktops are more easily upgraded. I've added a larger hard drive (it originally came with a whopping 40GB LOL!), swapped the CD burner for a DVD burner, and added a multi USB/Firewire port card. Some people like to upgrade their video card at some point. With an AIO, that requires a lot more work than a desktop does. Decide you want a nicer keyboard for a laptop? Forget it.
3. If you don't like the monitor, want to get a bigger one, or need to get it repaired, a desktop is so much easier. Unless you want to add a second monitor, with an all-in-one or laptop, you're stuck with what you've got. iMac screens are nice, but if it needs repair, the whole computer must go in.
4. Wires? Other than the monitor, what wires are you saving with an all-in-one or laptop? You still have to plug peripherals in. At least a desktop on the floor keeps them out of sight more. Besides, you can add an external backup or secondary drive to a desktop easily. With laptops and AIOs everything that can't be done with WiFi must be done with a wire. Try finding an internal TV tuner, backup HD, or Blueray Player for an iMac. The asthetics of any computer is mainly the screen and keyboard, both have more choices with a desktop.
5. Cost. Making things small enough to fit an AIO or laptop case, quality components tend to be a bit pricier. I bet a AIO/Laptop will run you more than a similarly speced desktop. Your budget of $2000 will buy you a pretty nice computer + printer (the guy who recommended uploading Walmart all your printing needs is nuts!).
Like Lee said, chances this is your "last" computer are not guaranteed as you never know what future technology holds, or how your needs will change. Having said that, if you want what you buy today to last as long as possible, I'd buy a desktop over an AIO or laptop. If you needs change, they're easier to upgrade or have someone do it for you. Same for repairs. If you can get access to their Business line, I'd look at something like a Dell Optiplex 980. They have a bunch of corporate IT stuff you don't need, but they're built well to last a while. Dell's Business side tech support tends to be decent, especially if you opt for ProSupport, which is 24/7 North American and short wait times.