+1 Yeah, replacing the steel rims with aluminum would be a worthwhile upgrade, especially for hilly SF. It may be simpler to replace the entire wheels. You certainly don't have to do this though.
+1 on the new brake pads.

IMO splurge on tires that are a little bit better than cheapest possible tires, as they make as much difference in ease of pedaling as the rest of the bike.


> 1.) I need rim bands, tubes and tires - what size and which ones to buy?

27 x 1 1/4, unless the wheels have been replaced. It should say on the side of the tires what size they are.

> 2.) I also need new cables - where can I find a set for my bike and is it a job I can tackle?

Not too difficult but it depends on your mechanical aptitude. You will need to readjust everything when you swap them.

> 3.) I see that most people get rid of the stock brake handles - should I do this or can I get parts for the old ones?

No reason to do this at all unless you want to waste your time and money in a failed attempt to make a Schwinn Continental look like a modern race bike. Don't do it.

> 4.) Chain - how does it come apart and should it be replaced for regular use?

Chain breaker tool. If it's rusty or stretched (google), replace it, they are cheap. Otherwise just clean it up, oil it and use it.