Welcome, @Paul Luna! I think you are making the right choice starting to think about buying vs renting. Buying will almost always put you ahead in the long term over renting, even if it's more expensive in the short term. As you just mentioned, rent rates increase, and your mortgage never changes. Also, glad you are coming into our neck of the woods. I have a few clients that have come here from Michigan.
As for your question, the best way to get your answers is not to seek them out by yourself. I would speak to a lender ASAP and see what is possible. I would first find yourself a great agent (one that is an investor themselves if you want to house hack or otherwise) and they will be able to walk you through the whole process and get you connected to a lender that will help you learn about your situation and what you may be able to afford.
As for the timeline, it depends on your situation and what you want to do. I'm going to disagree with some of the others in here, and say purchasing in the short time frame even if you plan on moving can be a good thing. If you are planning on moving at the end of the year, you could pick up a property in the Grand Rapids Area that would become a great rental, and once you move keep it instead of selling it and have it cash flow for you each month. The only reason I would stay away from purchasing in the short term is if you didn't have the capital reserves for purchasing now, and again when you move. If that's the case then I would stick to renting for the short term, save as much as you can and make sure you are in as good of a spot as you can be when you move out here. Get the process started early on out here and get connected to an agent (I am happy to jump on a call if you want), get introduced to a lender, and understand what it will take.
As for the BRRR strategy, that is a whole other item, but in short, you use short-term financing to purchase and repair the home to increase its value enough that you can refinance into long-term financing and pull out your invested capital. If you were selling in a short period you would more be in line with a live-in flip. But for your first properties, I would usually stick to something more straight forward.
