It's now possible to form an LLP in India. But is it a good option for a startup in India? Is it the right option when one partner may be from outside India?
There is no "stock" or stock options in an LLC. You can allocate LLC membership interests among co-founders, but providing providing membership interests to employees is not the same as offering stock options, and may result in you giving away more control over your business than you had anticipated. However your question seems to be about an India based entity so most of this discussion about US based entities is probably inappropriate to your situation.
Set up a US LLC, and then set up a corporation in India. When humanly possible, make the LLC a .inc. India can be a strange place to do business, depending on what goes wrong.
Not a direct answer to the question, but in the US, if you form an LLC as a single founder, you are treated by the IRS as a sole proprietor for taxation purposes, yet get the liability protections an LLC offers. If you are a single person the disadvantages (i.e. Double taxation, minutes, etc.) of forming a C or S Corp outweigh the advantages.
Also, I am not basing the decision to go corp solely along the lines of "investors won't invest in an LLC". You could always convert to a corp later. You can even form a corp that wholly owns the LLC.