It would help us if you could you let us know what you're planning to use your bike for: Commuting (and if so how far is it, what are the speed limits you're going to ride)? Days out? Rides with mates? Longer trips?
As for bike, get a 2nd hand Japanese 125, doesn't matter too much about age or mileage, as long as it has been looked after. It will be reliable, and won't lose you any money when you come to sell it on. Any that matches this description will do you fine, unless you're particularly short or tall, in which case you might have to look around to find one that fits your size.
Helmet: buy new. Go to a real shop where they sell one and ask for help getting the right fit. Without help, people tend to choose one that's too loose.
Other kit: buy secondhand from ebay. But what you get depends on what kind of riding you're going to do.