Hi there JP,
Thanks for your question.
First off, you are not alone! Its very common for students (not just international students) to have circumstances that result in attending an orientation that is late in the summer. Those students, just like you, have also expressed concerns about not getting into classes. But not to fear! For the most part, the University does a good job of projecting what incoming students will be wanting/needing to take, so I don’t think you will have any issue getting into classes generally. Furthermore, freshmen have to take seminars and introductory classes more often than not. This benefits you because seminars and introductory classes are HUGE.
If it really comes to to situation where you can’t get into the class you want to take this Fall due to a class (and all its multiple sections) are filled up, the great thing is that there is always Winter semester and Fall semester next year! I do not think you need to worry about falling behind, because the order of classes does not matter much in the scope of your 4 year journey at UMICH. For example, the Intro Biology sequence is BIO 171, BIO 172, and BIO 173, but you can take them in either order, with each other, or all separate.
To address your concern about not getting into a class with the “best professors…” I think it is great that you are considering the quality of your professors, but it may not ultimately matter. The reason I say this, is because if you are using online sources or peers to figure out which teachers are “good” or “bad,” what you hear will be just an opinion. What style of teaching that works for you may be different than what people online or your peers may feel. Much of how you do in a class will depend on your ability to work with the course (that includes the professor, GSIs, and external resources), not just the reputation of the teacher.
On the other hand, if you are adamant about taking class X from professor Y, you could be at an advantage by not being able to get into class X in Fall 2019, since fewer students will be vying for it in Winter 2020. Does that make sense?
Lastly, you will NOT always have the last pick on classes. The schedule for who gets to choose classes when is determined by the number of credits you have under your belt. This means that Sophomores will easily be able to choose classes before Freshman but not before Juniors. If you are coming in with AP or IB credits (let’s say you come with 15 credits) and you take 15 credits this Fall, you’ll have 30 cumulative credits. Then, if a fellow freshman who was lucky enough to have a June orientation/registration date came in with no credits takes the same 15 credits as you in the Fall, he will only have 15 cumulative credits. Thus, you will have “seniority” and will get to choose your Winter classes before the hypothetical freshman. 
I hope I answered your question and gave you some peace of mind. Best of luck, and please come see us at our Fall drop-in advising if you have further question!
Sincerely,
Lindsay (Co-president)

Hi there! I’m Haniyeh, one of the Pre-Med Hub’s advisers. I just wanted to add to what Lindsay said 🙂
First I would like to say congratulations on becoming a Wolverine! As a previous international student, I understand your concerns. There is a chance that some classes may become full, but there might be a waitlist for which you can register. Through the first three weeks of the semester, many students change their schedule and there is good chance that you move up the waitlist and finally get into the class. Also, I know that  the LSA saves some seats of the most popular classes specifically for the students who will register last. Additionally, during the orientation, you will meet with your assigned advisor and (s)he will help you to find classes according to your plans for future.

The other important thing to remember is that even if you can’t register for a specific class, you’re a freshman and you have four years ahead of you. Embrace this opportunity and try to explore other area of your interests. There are a lot of interesting classes that are offered by different departments and you can register for those while fulfilling the requirements. 

I hope this answer will be helpful to you. If you have further questions, please don’t hesitate to ask.
– Haniyeh (PMH Adviser)