Regarding your score, either nothing will happen or it will drop. Here are the key points.
So student loans are a different story when it comes to your credit score, the affect you if you do not pay them back on time or default on them. Now on the flip side they somewhat help you but not as much as a consumer product, auto loan, credit card, and etc. Now since they are guaranteed by the government they are not weighed heavily on consideration when it comes to product decision on rather not you’ll be approved. The main factor considered is the DTI, essentially all your debt obligations payments combined together, the less debt obligations you have the pay the more likely you are able to get approved, especially when it comes to Mortgages.
If you finance or shop around for a loan, expect your credit to drop a bit. If you only shop around for a loan or look for an approval on a loan, expect your score to drop a few points due to the inquiry. The nice thing is that this inquiry will only stay on your report for about 6 months.
If you decide to finance the vehicle and take out a loan, your score will drop. This is because of the inquiry, due to the new account, due to the increased amount of owed money, and due to your average length of credit decreasing. As previously mentioned, the inquiry will disappear after 6 months, but the rest will remain. The one benefit is that you’ll potentially make your mix of credit types look better. But short of that, expect your credit score to drop!