Buy 1 1/4" wide tires.
Paselas would probably be good, Michelin makes some too if you are cheap. Dynamic is the model.
You are going to need rim strips
There are grommets that allow you to migrate to presta valves.
The spokes, or lack of the spokes filling the nipples are of concern, that appears to be the front wheel...
Really wide range of take up of the spokes into the nipples.
While you have the tire off, a good time to true or have the wheel trued.
Check the spoke tension too... unless a spoke or two got replaced with a too short one... the spokes when of the correct length fill the nipple at least to the bottom of the slot
Otherwise the weak brass nipple is doing all the work