You should really ask an attorney about the cost/benefit of different options, but here are a few as I understand them, and why VCs generally demand a C corp structure. Standard disclaimer--I don't know what I am talking about and you are an idiot to believe anything I say.
Tax is a big one, and the reason I think that VCs don't like LLCs. LLCs are "passthrough" entities for tax purposes, like partnerships. They don't pay taxes....the members (shareholders) of the LLC pay taxes on their portion of the LLCs earnings or losses. For VCs and other institutional investors, this creates a nightmare from an accounting point of view.
C Corps are technically "persons" for tax purposes, and pay their own taxes. Much simpler....VCs are not in business for tax credits, they want capital gains when the successful investment is sold.
Governance--C corps have existed for a long time and there is a considerable body of law around them. Delaware is preferred because its laws are considered optimal (not sure of the details why), and its fees are low.
LLCs are very flexible...many of the governance elements are crafted into the Operating Agreement that controls the LLC, which is why LLC docs are much longer than the incorporation docs. I have always found that LLCs are more expensive to set up because of this.
So.....if you are going to take outside institutional investment, save time and start with a C corp...might as well do Delaware since every lawyer speaks Delaware law.
If you are not taking professional money, then you may prefer the tax efficiency of the LLC. You get tax benefits while you are losing money, and you eliminate one layer of income taxes when you are making money. This is assuming you distribute the excess cash--if you don't, then you have to pay taxes anyway, but you don't have the cash to help. For this reason, most LLCs make what is called a tax distribution to help members cover their tax liability.
There are other structures (sole proprietorship, S corp, partnership) that have pros and cons depending on exactly what your aspirations are for the business, but C corps and LLCs dominate.