For a recent graduate like you, I think a startup would provide you the best opportunity to learn, expand, network, and make a niche to something you have the passion at.
Talking with the clients to gauge how they feel about the company could be a good aid in your decision making, but ultimately, you would never know unless you actually jump right into it.
It is quite hard to compare a full time position with an internship based on a lot of factors which satisfies your requirements. Some people may find internship better than full time salaried positions because they find the latter more enjoyable and goes in line with their values in life.
Good luck on your decision. You should be able to make the right choice.