1mm is pretty standard. Just make sure you get electrical solder not plumbing solder (plumbing solder has very corrosive flux).
For lead-free you'll want close to 400C.
If you are a beginner, though, leaded solder is quite a bit easier to use. FYI, the switch to lead-free is for the environment, not safety, if that's what you are worrying about. All critical devices are still made with leaded solder for reliability (no one knows how reliable lead-free solder is, yet, because it hasn't been around for that long).
If you are doing a big production run, lead-free could make sense if you are environmentally conscious, or want to sell your product in Europe. For prototyping and hobbyist work, the environmental impact is negligible, and leaded solder is a lot easier to use (flows better, melts at lower temperature, etc). But it's up to you.