The best option for start-ups, as it is the only business structure that can raise funding from venture capitalists. An added bonus is that promising employees can also be given equity stake in a company via ESOPs.
The LLP has the same set-up as a partnership firm, but many of the advantages of a private limited company. It is also cheaper to start and fewer compliances.
An OPC, as the name indicates, has just one partner, but enjoys nearly all the advantages of a private limited company (though raising funds would be tough). A major drawback, however, is that it must be converted into a private or public limited company in case revenues cross Rs. 3 crore.
All it needs is a partnership deed that does not even need to be registered. A good option for home-based businesses, particularly while starting out.
Small businesses with little to no risk can run in the name of the owner itself. You can simply pick from one of many government registrations that apply to your business to get started.