penny3333's advice is good: it is difficult to recommend a cruise line to someone you do not know. A good agent can give you good information on all the cruise lines and help you decide which one suits you best.
I personally would not want to cruise with four in a cabin. Kids are big today; a 12 and a 14 year old are practically adults. It can be done but it would be pretty tight. Two suggestion: a jr. suite or mini-suite would give you considerably more room and a larger balcony. You still have the problem of only one bathroom; but at least you can streatch out a little. Or what some families have found best is an inside cabin for the kids across the hall from the parents in a balcony cabin. Kids don't spend much time in the cabin anyway; and it gives you the convenience of a second bathroom--and you can all share the balcony.
As for bar prices, they are all about the same--HIGH; there is just no getting around that. Most lines offer some sort of soda card which can save you money if your kids drink a lot of fountain drinks. And there is usually some sort of drink "special" every day; but adult beverages are expensive and you can not bring your own, except for a couple of bottles of wine.
There will be lots of children if you travel on school holidays; but most lines have excellent youth programs to keep the kids occupied. Unfortunately not all parents utilize these programs and some kids just run wild. But this is a hit and miss proposition. If you are thinking of a Med cruise, try to avoid July and August as this is when most Europeans are on vacation and the tourist sites ashore are jam-packed.
I hope this helps a little.