In my opinion, your career in a sense starts in college. Although it is not the end all be all, internships/research positions are where your individual experiences start and they are a great place to figure out where your interests lie. In my personal experiences, I have worked as a Lab QC intern in a chemical engineering company, done software development in a research position at NJIT, and have done analytical testing at a pharmaceutical company. My interest lies in pharmaceuticals and in a sense, I was able to figure this out over different experiences. 

Considering the size of the companies, I believe for your first job you should try to start at a larger, more reputable company. This is not necessarily a requirement, but the benefits and potential for increasing pay, increasing your job position, and working your way up are much higher in a larger company than in a smaller company (generally). Also, there is risk with smaller companies because a lot of the times they have high chances of getting beat out due to competition or just bought out, and then the companies' structure can change, and you can lose your job (happened to me with my first internship at the chemical engineering company). Specifically in the field I want to go into(pharmaceuticals), this is common so my preference would be a larger company. Smaller companies are however, more tightly knit in that everyone knows each other better (as compared to a larger company where you may not interact with the people as often, but it does depend on your department and where you are working). However, from my personal experience working at a larger company has many more benefits and relatively more job security as well as opportunities to move up.

I'm much more partial to the smaller company for employment. I've had multiple internships, two with a large company and one with a company of 30 people. I much preferred the company of 30. The pay wasn't as high but it was still reasonable for the industry. Beyond pay, I think it really gave much more of a learning experience than a larger company. For example, there were only 4 engineers, including myself, and it was common that I'd be tasked to a project for days or even weeks at a time where I was the only one working on it. This experience taught me way more in terms of device design and considerations as well as overall project structure and management than my months working at the larger companies. Working at the smaller company felt more like a mentorship, like my coworkers cared about my success, and the success of everyone else in the office while the larger companies I only felt like a cog in the wheel with no guidance.