Hi Again non-Savvy --
In advising on cars, It would help if you were more specific about "children." (NOTE: Progeny aged 24 are not "children" they are young adults, size-wise.) We're smart but not mind-readers. 2 young male twins, of basketball-player size, that's a challenge. Female twins, 5' 4" or 5' 6" No problemo. See what I mean? If your 4 people are normal size, You should look at getting a full-size 4 door sedan.... something like a Honda Accord. If 3 are over-size, a premium model such as a Merceds 4-door will have more legroom. You will not have the choice of renting a cross-over model, in many fleets, the choice jumps from Sedan to a biggie with rows of seats, seating 8. Clumsy to drive/park.
As Rosalyn says, often those fleet descriptions will underestimate luggage capacity. In past, renting an Accord-type sedan, we easily fitted in 4 20" rollaboard bags, and a couple of backpacks (daybag size) in the "boot', and the 2 people in the backseat handled the other 2 daybags, either by their feet or in their laps.
I am not sure what you mean by a "suitcase"??? I consider a 20" rollaboard to be a "suitcase." Does your wife mean something large, or is it a garment bag? What I have listed here is the reasonable limit. If she wants something more, ask her whether she's willing to hold it in her lap or on her shins the whole way. If she's taking another large bag in order to have something dressy, tell her that NOBODY dresses up in Greece in hot weather, and especially NO extra shoes. 1 pr STURDY sandals, 1 pr walking shoes, maybe 1 pr lightweight flats. NO heels.
Yes, it's good to rent in advance, and MAndatory if you want automatic-shift (many fewer of these, since 99% of Europeans drive stick-shift, because of higher petrol prices). However, in the 8 trips where I've shared a car rental w. companions, we've never had to pay ahead and get vouchers; we do give them a Credit-card # to hold the reservation, but it's not charge until we show up. Several times we, like stanbr, used ACR at Airport and very satisfied w prices, service and condition of cars.