We kept our boat out in the Balearic's for 2 years and carried a small sib as a tender to carry 2 adults and 2 young children.
To try and answer your questions. First of all the Med isnt always the beautiful glassy watery playground that it looks like from the shore, it can get very rough, especially in the afternoons. Bare this in mind when picking a boat.
I would suggest for ease of storage and assembly go for an airdeck and to make sure you can always get home safely look for decent sized tubes. Take a look at Bombard 380, HonwaveT38, Zodiac Futura FS Mk2 etc. These boats are a decent size for a sib, but they are not light and will need a couple of adults to carry them.
To give them the performance you are looking for you are going to need 15-25hp, look for Yamaha, Mercury/Mariner or Tohatsu. Go for a 2 stroke, they are lighter and simpler.
Transport is going to be an issue but you can put transom wheels on the boat to move it short distances or use a folding launch trolley. Sorry, have no idea about "cheap" storage options, that's not a word I came across very much in the Balearic's
. Leaving a sib in the water without anti fouling even for just a couple of weeks is not an option, it will grow a beard incredibly quickly and reduce performance significantly. Daily scrubbing may help this, but not a lot.
You can land on beaches in small boats, but you must use the buoyed tender channel, apart from this channel you must stay offshore of the yellow swim area buoys.