I would say Germany or France fit your bill best from the well-traveled countries.
Beaches: Germany's beaches are mostly limited to the north if you want salt water, but there are tons of inland beaches. We like that sort of thing here in Germany. France has a lot more coastline, from rocky in Bretagne to Mediterranean ones in the south. Advantage France.
Castles: Well, Germany has that covered. So does France.
Mountains: Again, both have that covered pretty well.
Great food: Advantage France; depends a bit on what you like, where you go, and your willingness to seek it out in Germany.
Beautiful countryside with quaint villages: You'll find that in both.
Friendly: I would say outside Paris it's a draw. If you count Paris, advantage Germany.
English speaking: Advantage Germany.
History: You'll find it in both.
Budget: Depends on what exactly you want. Both can be done well on a budget with prior research.
UK/Ireland:
You won't find true mountains in the UK/Ireland, but you will find places like the Peak district that will probably be enough for your requirements. But you'll have to know where to go for "mountains."
The UK/Ireland option won't win in the food category (except London, with its immigrant/colonial import food scene).
Budget: Ireland is cheaper, UK traditionally slightly more expensive, though recently less so.
Obviously a win in the language category.
Italy:
The castles are of a different type in Italy, so do your homework there. Might I suggest a day in San Marino?
English: In places like Rome or Venice or San Marino, no problem. In those quaint villages, it gets trickier (that's true everywhere, but as far as language I would say Germany is the non-UK winner of those on your list).
Budget: Italy's cities can be pricier, so planning is required.
A few other considerations: Weather. Consider how well you each do with heat, rain, etc. If you need warm, then Italy or southern France are your best bet. If you prefer milder weather and are heat wimps like me, I would avoid Italy in the summer. Also, your sense of adventure in terms of dealing with the unforeseen or less-than-efficient. If you think unfamiliar and a bit confusing is fun, Italy is great. If you are conservative and just want to relax together as newlyweds with no problems or issues, the UK/Ireland or Germany options are best.
Finally, my ultimate suggestion for what you want might actually be Slovenia. Maybe add in Croatia (or Rome if that's super important to your fiancee). I think it might fit your bill most completely.
