Well, keeping the drive train clean is always a good idea.
As for the tires, check them for dry rot, but if they look good then don't worry about using them. If you need new tires, you'll have trouble doing better than this:
http://www.ribblecycles.co.uk/sp/roa...re/CONTTYRF321
Your saddle looks like it's tilted down (should be level) and those bars give me the heebie jeebies - looks like the previous owner tilted them up a lot, and also moved the shifters up too high on the bars. The bars are also mounted really high (as in spacers under the stem, and the stem is tilted up instead of more level) but that's a personal preference thing. I'd ride it as is and then tweak it after a month or two if you want to.
Is that saddle the right height for you?
For now I'd just clean it and ride it. put flat pedals on if you're worried about the clips.