No chains. If you do not have a trusted jeweler, ask people in your area for recs. Agree on quality over size. Hopefully, your fiancee understands that too. Remember the importance of the depth of the diamond. A big, but flat diamond will not shine like a smaller, but deeper one.
No one can answer how much you should spend. Spend as much as you can afford. As Across said, do not be stupid though.