Get tickets on line ahead if you do this independently (which I think you should -- there is absolutely no need for a tour to do this) That lets you enter at the group entrance instead of waiting in line or at the regular entrance also without waiting in line.
Just get the train from Rouen to Vernon and get on the shuttle bus to Giverny. You buy the tickets on board. Step lively because this bus does get full (well it does from Paris -- not sure it is as big an issue from Rouen) Or you could bike as others have suggested. I think it is a bit far to walk but with a picnic it would be a nice walk.
Once inside it really doesn't matter how crowded it is. It is beautiful and you will be able to pause and enjoy the sights you want to see. We found people very gracious about taking turns at photo ops and so forth.