You certainly do not want to miss Keukenhof - suggest you go on a weekday as it is busier on the weekend. This is 80 incredible acres of flowers including a stunning display of orchids. Consider spending the entire day; you don't want to be rushed. You can get there on your own or sign up for one of the buses that go to the gardens.
A word about the crowds. Yes Keukenhof will be busy. But it is so spread out the only crowding we actually experienced was when we went to eat lunch. When arriving, head to the back of the gardens and work your way forward - it will also be less crowded.
The Alsameer flower auction is open weekday mornings. It is located near the airport and there is a section in the RS Amsterdam book on the market. You can get there on your own and go through the market. Maybe pair the auction with with another activity in the afternoon?
You want to have plenty of time to wander through Keukenhof without being rushed.
The tour you mention sounds like a good possibility; however, would inquire as to how much time they actually allow you at Keukenhof before committing to the tour. We had about 5 hours which was just about right for us.
Enjoy planning and have fun!