The current low level Mac Mini with an upgrade to 4GB memory is probably the best bang for your buck. That's what I have except with 8GB; got my memory from Amazon for $130, cheaper than Apple memory. It's a very capable machine. If you use a lot of programs simultaneously, the standard 2GB is kinda cramped, but 4GB would do fine; it just seemed like a good deal for 8GB and I use more than your average number of apps simultaneously and lots of Safari tabs.
The new MacMini is much nicer than the 2009's. I know this because I had one before this one; with 2GB of course :).
You're gonna love OS X by the way. Don't be surprised if you ditch Windows in a year.
About your specific questions:
Any current Mac has an Intel CPU. Apple switched from PowerPC back in 2006 and yes you need one, but you don't want a computer that old anyway!
Just about any keyboard or mouse will work fine with OS X. If you are using some kind of fancy mouse or keyboard, then you'll probably will need some third party software to get all those custom parts working, but all the standard parts will work; left click, right click, scroll wheel, cursor control etc. There is a chance however that there is no OS X equivalent of the third party software you may be using.
Finally, Macs work with standard monitors and even regular modern TV's with DVI, VGA, HDMI inputs (virtually all of them do). The most you'll ever need is a common adapter found at Best Buy, Apple Store etc.
1GB of RAM will kill you: frankly, I can't imagine that it would meaningfully run. I'm currently using a 2009 MacBook (not Pro) with 4GB of RAM, and for the first two or three hours Xcode runs pretty well.
After that, though, it gets slower and slower. On a pretty small project Xcode will be using multiple gigabytes of RAM with the OS swapping 2-3GB to disk. Before long I not only have to quit Xcode, I also have to restart the machine to get things back up to speed. (To head off potential commenters, no, it's not something else on my system, it's Xcode 4: no other piece of software, including Photoshop operating on a 20+ GB file, fails to clear up the swapping speed problem after quitting the app.)
I can safely say, both from my experience and from talking to others, that 2GB of RAM is the bare, bare minimum, and it's not going to be a good experience. I'll be replacing this system soon, but in the meantime I'm upgrading to 8GB because I'm losing too much time to only having 4.
Best Answer
Today, I'd go with either a 15" or 17" MacBook Pro. They would allow you to work with the iPad simulator at its native resolution. It's a bit too big to run full-size on the 13" models, so I always end up running it at half size, which is less than ideal. Even if you're not planning to develop for the iPad right now, I'd still plan the hardware purchase around that possibility. The likelihood that you'll do iOS development and never build for the iPad is pretty low.
Beyond the simulator issues, I like to have the largest screen possible when I'm programming. I have a 13" MacBook Pro, but I connect it to a 24" monitor when I'm at my desk. If you're like me, the 17" would be ideal, if you don't want to have a second screen.
However, Apple is holding a Mac-focused special event tomorrow, and it's never a good idea to buy a Mac this close to one of those events. The entire laptop line is due for updates, and there has been (unconfirmed) speculation that any new models may run at higher screen resolutions, especially on the smaller end of the range.