As Marc Andreesen wrote, you want a fast grower. If the company is growing, there will be plenty of opportunities for you to grow with it. If it isn't, you're fighting over a fixed-size pie with every other employer.
LinkedIn/Dropbox/Square are great choices today. But so are Google, FaceBook, or (if you get into one of their growth products like AWS) Amazon. I've been with Google a bit over two years and am already more senior than 60% of employees. And my job description is anything but set in stone; it seems to have changed roughly every month for the past year, and I have a lot of latitude to set it myself.
LinkedIn/Dropbox/Square are great choices today. But so are Google, FaceBook, or (if you get into one of their growth products like AWS) Amazon. I've been with Google a bit over two years and am already more senior than 60% of employees. And my job description is anything but set in stone; it seems to have changed roughly every month for the past year, and I have a lot of latitude to set it myself.