First, can you get by on English and a little German. It depends what you mean by get by. Many people study English but only a few really speak it. So, you will be limited to the number of Hungarian friends that you make (but you should make some). German is a useful language to know here.
Do you need a car? Not in the city itself. There is a good subway and tram system augmented by busses.
Cost of living? Food for my wife and I (which we prepare at home) costs about $100/week. A reasoable apartment will rent for $350-450/month with another 50% on top of that for gas, water, electricity, tv, etc.
Beauty? That's very personal. I don't know what you like. The main street, Andrassy, is on the UN Heritage list as is the Castle area. Most of the buildings in the main part of town are about 100 or so years old, grand, in need of repair, and remind one of the Kaiser and pre WWI times. But, although I don't know if you'd call it beautiful it is interesting. And its only a few hours by train to Slovakia and Austria.
Trains are inexpensive and enable you to take many day trips.
View camera? Why not. Although I haven't seen any in use here Hungarians tend to let people do what they want to. So I doubt if anyone would bother you.
A good source for apartments, etc. http://www.budapestsun.com