Hi Hindugirl and Graceful.
I couldn't really say how much it costs to come over here as a student and get by since I haven't done it that way. But I can tell you that if you are going to be living here in London, plan on it being a lot. The cost of living here is incredible.
Rent alone is upwards of about £800 a month for a very small flat on the outskirts of London. That's right around $1400!!
As for how much you need to have for the marriage/fiance(e) visa, there is no set amount. I had about a $1000 in my bank account and was granted the visa, so if you go from that, you don't need that much. More important is what your future spouse has and can provide before you are married. The longer you plan on waiting to get married after you arrive, the more money you'll need to have saved up to show you can support yourself without working. We got married about three weeks after I arrived, so that probably has something to do why I didn't need much cash.
Anyway, best of luck to you Hindugirl! It wont be easy but I'm sure it'll be worth it!