ill second that the best tire is the largest that will fit. If you think a 28 will fit, then start with that. For commuting, I wouldn’t recommend anything less than 28. There are some measurements you can do to give som approximations on what size tires will fit, but there are a lot of variables here that can affect that, like the width of your rims, wether your chainstays are dimpled for tire clearance, if your tire brand choice lists their sizes accurately, will the tire stretch (what PSI will you be running). Will your brakes clear larger tires? (Most modern dual pivot side pull brakes are designed for lightweight and aerodynamics, not for tire clearence)

What tire size you run, is obviously a personal choice, but as a full time commuter for years, my advice in this regard is pretty simple: don’t run less than 28mm, even if you’re a lightweight. If your frame can’t fit at least a 28mm then you need to accept that it’s not a good choice for a commuter. If it can accept a 28, then from there you can do some measurements to see how large a tire you can run. If you can go larger, do it. I get the rationale behind bicycle commuting to save money, and so you’d not want to spend very much, but a commuter bike is also a tool that you are going to be relying on, and if it’s not up to the task, you’d only be giving yourself unnecessary headaches down the road.

as for what type of tire to run? Well schwalbe is regarded as the king of commuters and they have several good choices. (Such as the venerable Marathon Plus “flatless” tire)
https://www.schwalbetires.com/bike_tires/road_tires
my advice though, is that unless you live somewhere that you know you’ll be susceptible to actual punctures, (plant thorns, streets or bicycle lanes full of debris, etc) you probably don’t need serious puncture protection. Most people don’t suffer actual punctures as much as they suffer pinch flats. There are two main ways to get a piinch flat: 1. Riding on tires that don’t have enough volume to support your weight and the weight of the bike and anything you’re carrying) 2. Not having your tires at a high enough PSI. The smaller your tire, the more PSI you’ll need to avoid pinch flats. The more PSI the harsher the ride. Pretty simple. Potholes cause pinch flats, not punctures.

your fork will likely clear just fine. It’s your chainstays and possibly the brake bridge that will usually be the issue. measuring clearence between chainstays can be pretty tricky. If your commute is that short, then it’s possible that you may not need to do anything to the bike. If it comes with stock 25mm tires, then buy a cheap set of 28’s, or possibly go to your local bike shop or bike co-op (if you have one) and ask them about tire clearence. They might even have a wheel with a 28mm tire mounted that you could use to test fit. I would look into this before spending any money. I don’t know what your weight is, but in my opinion, there’s no logical and certainly no comfortable reason to be running 25mm, even for a short commute.

I dont know anything about Tektro 510a’s, but if im not mistaken, with tektro, anything in the ‘500’ series should be a mid reach brake, so I would be surprised if they didn’t have ample clearence.

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Sounds like this bike has more or less, the same clearence as my bike. If so, a 35 would be absolute max, a 32 would be a very good middle ground choice (I run 32s on my commuter) and a 28 would likely allow you to fit full coverage fenders, if you feel you need them. Go with 32s, upgrade the brakes if you need extra clearence and then you should be good to go.

i personally ride panaracer tires, so a few recommendations I can give, (all come in both 28 and 32mm)

panaracer RiBMo - if you want a good balance between puncture protection but lightweight and fast (slick)
panaracer T-serv - for a similar tire, but with treading for more confidence through dirt/sand/gravel
panaracer Tourguard Plus - for a heavy duty puncture resistant tire
panaracer GravelKing - for a fast, lightweight, smooth tire at the expense of serious puncture protection (my favourite tire, and what I commute on)

happy riding, cheers mate.