Well, I'm not a travel agent with access to cruise fares but I can tell you that with that budget you may limit yourself from a couple of those choices. Coach airfare for 2 from Chicago to Rome cost us about $2800 in June. We probably spent about $2500 to $3000 on excursions and expenses on the ship, that leaves with roughly $6000 for the cruise itself. Regent and Seabourne are going to be high end cruises (a really quick check with regent has the cheapest cabin at $3895 per person for a med cruise) I would suggest you consider a Royal Caribbean Cruise, Princess or even a Holland America cruise. Each have cruises leaving from Rome.
For $3000 each you can get a very nice cabin on any of those.
Holland America Lines tends to attract an older crowd where as Royal Caribbean and NCL will have more families on board. Your other choice would be Celebrity cruise lines. They would be a great compromise between the high end lines in your list and the more moderate cruise lines I have mentioned. But I'm not sure if they have an itinerary that departs from Rome.
$12K is very doable. Find a travel agent and start checking into prices. Tell them you want a Med cruise departing from Rome and to have them give you a Balcony cabin price for the lines I have mentioned. You can assume about $3000 in "spending money" above your airfare and cruise total to determine which to choice from.
If you get a couple of choices from the agent, then come back here and spell them out and we can easily give you information on your choices.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013