The first thing that seems to "go", at least visually, is the chain (rust). If you find that you can't keep the rust away on it (and you should be able to, with proper lube), you can replace it something like a KMC X8.99, which is nickel-plated and should be very resistant to corrosion.
I would keep your seat post lightly lubed so that it doesn't get stuck in the seat tube, especially if you never move it. I'd also keep the stem lubed and move it every now and again (if it's a quill type stem), so it doesn't get stuck.