Company

You have a obtion to get a Private Limited Company and if you want that company can also take over business of your firm if special clauses are contain in its Memorandum. As you enquire a private limited company neither raise money from general public nor can transfer its shares freely.

Answer of your second question that how to procede for incorporation of a company you will need help of a professional, but i can give you some brief of it:

at least you need 2 person who will be first director and shareholder of the company,

name of your proposed company which does not exist before

DIN and DSC need to be got for first director and other form filing formalities which could only be done by a professional who may be a lawyer, CA or CS