Suggestions for types of investment and retirement accounts, and how much you should put away?
Anything that gives you a tax break basicly. This becomes "free money" in a sense. I think the big three would be 401, IRA, and a HSA account (if offered). To start with, always take the match the company provides. Once you figure out your day to day expenses (some reasonable play is fine, just don't count on fancy cars and steak diners every night), start to put some away for rainy day funds (balance interest rates with term lengths and flexibility). Once you meet your comfort level there then max out the 401, IRA, HSA, etc contribution. Retirement accounts can grow for you some via interest and market swings, but they grow faster when you contribute to them.
Don't forget to keep adding to your rainy day fund though, that new car may have a higher payment or replacement cost and quickly move a 12 month buffer to a 8 month buffer. However, if you start finding a 16 month buffer then you may have a nice new shinny in the near future and make you happy