Celebrity is top of the line for cruising! You will love the experience. We were on the Horizon last year for an adults only cruise & it was by far the best cruise we have been on. I have heard that the Millenium is a nice ship. I think any Celebrity ship would be top notch.
We did the Mediterranean 3 years ago on the Grand Princess. Flew to Venice and met the ship there. Went to Florence, Italy; Capri, Barcelona, Portugual, Monaco - probably some of the same ports you will be going to. Let me know if you would like any info on the tours we took. It was a most unforgettable experience and I can't wait to go back to Europe.
You will truly have an awesome trip. Good luck.