I would have thought touring bikes, either UK/US style drop bar or european style flat (or trekking) bar, would be a good choice.
The UK would appear to have a LOT of touring bikes available; Orbit and Edinburgh Cyclery might be cheaper than some of the other options; Thorn has a good rep, as do Roberts and Dawes and Mercian and Bob Jackson. Canada and the US also have excellent selections which you'll find on this forum eg. Surly LHT, rocky mountain Sherpa, Trek 520, Fuji touring, Cannondale touring.
Xilios is a forum member with experience cycling in and to Greece. He might be able to help you with route selection. I'm not sure if you'd wand to go along the Dalmatian / Adriatic / Ionian coast, or by ferry from Italy. Also, have a look on crazyguyonabike.com for anyone who's done what you are planning. I'm sure there are many who have done at least part of it.
Is your wife also keen? If so, start doing longer day trips on the weekends, then some weekend-long tours, then one or two week-long tours, and if you both enjoy it then go for it. You need to work out your riding patterns for the day, and how to sort things out in camp. Also things like maintenance/repairs to the bikes, laundry, cooking, dealing with minor injuries and strains.
Have you considered a tandem? I like riding a tandem with my wife, but it isn't for everyone. Give it a go locally by hiring one for a day if you're interested.