There are tons of tire choices with a multitude of opinions.
Light tread like on the Marathon tires may or may not make a big difference. I thought my Marathon tires had better climbing traction on my driveway (with a few fir needles) than other slicker tires. However, I'm not sure how much was tread vs grippier rubber.
Anyway, there is no reason to avoid tires with moderate tread, and they do give a quick visual on wear.
I do most of my riding on 25mm tires. I did recently do some experiments with some quality 35mm tires (Clement X'Plor USH 120), and was surprised to find very little difference in my peak performance vs my thinner tires, although I might not choose that as a commuter tire.
The one thing I would encourage you to do is to choose puncture resistant tires.
The Marathon tires are HEAVY, and unfortunately I snagged a big piece of glass with mine early causing significant damage.
For low cost tires, I've been very pleased with my Origin8 Elimin8er tires. A little heavy, but not bad.
Continental has a number of popular tires including their 4-seasons tire, and Gatorskin and Gator Hardshells.
Compass does sell moderately wide tires with a moderately smooth tread, but, they appear to be more of a performance tire than a commuter tire.
https://www.compasscycle.com/product...ts/tires/700c/