...The TC looks appealing now as I have Applecare on my Mac mini and it says it covers a TC also.
My assumption was that the internal drive on the TC would be much quicker than USB 2.0, but it's not.
You really are just paying for the simplicity of it all, because time machine works in the background and you hardly notice it. I don't think the speed would be an issue in hindsight.
I was considering a second hand Mac mini as another option, with server. I'm starting to think I should only put OS X server on the Mac that is 'the server' and nothing else if I go for that option.
Yah, simplicity. The TC is a really nice product.
However:
Maybe my usage is more arduous than most, but I've had two TCs fail. As you note, they're covered under my various Macs' AppleCare extended warranties, so there was no problem getting them replaced. The first time it happened, the current-generation TC and Airport Express (with its new Time Machine capability) had been introduced. My failed TC was of the previous version, and because I was losing terabytes of backups I requested that the failed TC be replaced by a new Airport Express. But, that went against policy, so I received a refurb TC identical to my old one.
So, I got it home, and went through the slow process of re-backing up all the machines that had had information on the previous machine's hard disk.
And then it failed AGAIN. (Both failures had to do with routing functionality rather than the internal hard disk.) So, back to the Apple Store, rather annoyed. This time I really protested losing my backups twice in as many months and begged them to replace the TC with the Airport Express. This time they made an exception to policy, and so I went all-external for my backup needs.
Which is why I recommend that approach. It's like any other all-in-one product: every time a formerly modular function gets integrated, the overall chance of a failure of the whole device increases.
Right now, if one of my external backup drives fails, that's as far as it goes. If my router fails, that's as far as it goes. But when a Time Capsule fails, you lose terabytes of backups.
Just be aware of that. Your luck might be better than mine was, and I hasten to admit that nothing truly bad came of my experience. But it could have, especially if I did not have duplicative backups.
(I also use Crashplan for remote backups of my most important machine. I'm a bit of a freak in that way...)