I'm a strong believer in the philosophy that you need to walk in the door knowing you want to work somewhere. If you don't know already then you've done insufficient research or are insufficiently motivated and it will show.
Starting right out of college I picked where I wanted to work first and then started making the connections to make that happen. I always volunteer to work for free prior to getting hired. Why? because a work-to-hire internship, no matter your level of experience, is better for both you and the company. It's especially good if you don't fit the traditional resume of someone in the role for which you're applying. This works especially well with startups since their hiring practices are flexible and they are cash conscious. Four out of my last 5 jobs have been landed like this, the other I was recruited.
You should be excited about the specific company you're talking to. You should want them to succeed from day one. This will make you stand out from the crowd of "job seekers." You're not looking for a job, you want this job and you're ready to buy.