It is far easier to move from a large company to a small one than the other way around. So if you change your mind later on, it will not be difficult to find a job in a smaller company.
Large companies introduce to you to the entire spectrum of talents, creativity, support and line positions in a given area. It is where it’s happening: the best and latest ideas, the smartest people (and the hardest working).
It’s also easier to move laterally — from one big company to another.
The petty tyrants and malicious fools that crop up in a lot of companies are easier to handle in larger companies too; they very rarely are the bosses, and there are formal and informal systems in place for isolating and rendering them powerless!

That depends on what you want. The company you describe would offer significant challenges and room for growth– but also relatively high risk. A small, established company would offer the least risk and (often) the least stress– but there’s no room for advancement. A large company is often the place to get your feet wet since you’re likely to have the opportunity to gain a variety of experience– but there’s less job security than there used to be, and you rarely get to see the big picture.

My own path started at a huge company, worked there for ten years, and then struck out on my own. I’ve been self-employed for 15 years now and love it– but the experience I gained at a large company laid the foundation.