To start, I strongly believe that completing an internship is more valuable than a ML related summer research project, unless that research is done in the context of a respected laboratory at your university, and you have the explicit goal of publishing a paper that will help you gain admission to top graduate programs in machine learning. With that said, while internship roles in data science at tech companies are plentiful (see, for example, What companies have data science internships for undergraduates?), finding companies that actively hire undergraduates is non-trivial. You'll need to be aggressive, sometimes applying for and following up with recruiters on roles in which a graduate degree is recommended or even required. Finding companies that are willing to take a chance on a younger candidate will be an inevitable filter luckily, several great companies are willing to engage with undergraduates. I evaded this artificial barrier by interning as a data engineer, and working on infrastructure related to the data science team. This gave me valuable insights into the day-to-day efforts of a data scientist.
Secondly, I highly recommend choosing to work on a product with which you have some familiarity. This is the most underrated element of the decision-making process, in my opinion. As a data scientist, you will constantly be called upon to generate and test hypotheses about the product, produce insights, and suggest future directions. If you're an active user of the product, this isn't nearly as difficult in fact, it's often fun! Targeting companies that create products you love will make you a better interviewer and a better employee.
Finally, have learning objectives. Goals will dramatically change the roles and companies to which you apply. If you want to create scalable machine learning systems, a role in data science probably isn't right for you instead, you should target ML engineering roles. You should also identify, and interview with, companies that have established a positive reputation for using machine learning systems to solve problems. If you want to work directly on business problems, you should target analyst or quant roles, and an entirely different set of enterprises. If you're interested in learning about how Internet companies prevent spam and abuse, data science roles at social media companies may be most suited to your learning objectives. Setting learning goals also has the benefit of preventing bad fits (a situation in which you're working on projects that don't interest you, to the detriment of both parties).
To summarize, successfully navigating a data science career is probably not so different than managing a career in any other field: set some goals, be aggressive, know your worth, figure out what's fun and what isn't, reset those goals, and repeat the cycle.