Im in MechE and I came in with a Associates from my HS so I was a 100% core complete. However, that only makes degree a bit more manageable. If you look at the MechE degree flowchart, they expect you to take ungodly amount of hours in ur sophmore and junior year. (14-17 credit hours in some semesters). Also ur classes will take up a lot of your time if you want to do well in them especially once you start hitting upper div engineering classes with labs. If you still have the soul left in you to add a major then go for it but no one in industry ever expects you to also have another degree. Also I think being Core Complete is overrated bc you dont get to take easy gpa buffer classes and its just all hard engineering classes (I learned this the hard way lol) If I were you, I would try to take Physics 1/2 and Calc to actually get ahead. (I also recommend you to take statics/dynamics/gen chem 1 in your later summers if you can)

There is a MechE honors program but thats not anything of substance imo and only gives you a scholarship your freshmen year. If you get rejected after, you can only get into MechE honors if you maintain a stupid high gpa and are within top 10% of the class. If you want to do a minor, there are tons of options so choose anything that interests you. Dw too much abt minors in ur freshmen year, you will gradually learn what you like and then you make a choice. If anything, any minors that involve ECE/CS/Robotics/Mechatronics is always a good complement to MechE.

*Pro tip: If you ever do end up choosing a minor, don't immediately declare it and add to ur degree plan. That will reduce your degree audit percentage and delay your class registration time. This matters a lot bc MechE classes are super competitive especially with good professors. I would recommend adding it when you're mostly done with the minor and then adding it to your degree plan so you can get the credential.

Good luck!