Get the First Class medical.
On my initial application for a First Class medical, I wasn't qualified and had to get a medical flight waiver for vision (took an entire year for the process) and had to do extra testing for a congenital heart murmur.
This was pre-solo back in 1987 and it was almost a 'career moment'. Luckily, if I had to 'wrap it up' because of my inability to qualify for a First Class physical, all I had invested at that point is a lot of dreams and a Jepessen Private Pilot ground school kit.
I got issued a Second Class OK, while waiting for the paperwork to process.
The mumur went away in 8 months, and I finally got my sh*t together vision-wise so I didn't need to use the medical flight waiver any more -- but if I was a fresh graduate of flight school with a fist full of loan payment coupons and couldn't qualify for a First Class physical, it would have sucked.
Trust me, get the first class physical day one. That way, you'll have time to clear up any maladies you might have or learn early enough if you're going to even be able to qualify to be a part-121 pilot.