First off welcome to PW!!!! And congrats on your engagement.
Now on to your questions:
should the couple spend a fortune on honeymoon?
It is honestly different per couple. What you can afford to spend. Some can't spend too much, others can. Personally I think a honeymoon is not like any other vacation so I splurged more than i would on a normal vacation.
how long should one spend on honey moon?
Again another personal question. That can depend on where your going, how much time to take off from work..etc..
where is the best place?
Another personal decision. Where have you wanted to go? Are you beach goers? Do you want all-inclusive? Are you more of history buffs? Are you nature lovers? Are you a party couple? Are you a private couple? Do you want to do alot of things? Or
are you content just laying around?
We went to St. Lucia since it was a good mix of nothing to do with fun things to do.
by the beach or in the greens?
This again depends on the couple. What do you like to do? Are you more beach goers and just want to relax on the beach. Or would you prefer something more secluded and shaded on a mountain. We did both. Our Resort (Jade Mountain) was on
the side of a mountain so it was very lush. The beach was at the bottom of the mountain so we just needed to walk or take a quick shuttle to the beach.