If you want to ride up kerbs it would be best to have the largest diameter, widest and toughest tyres possible.
For a short period in the mid 1980's I had a job driving urban buses, so had to frequently drive over kerbs, mainly to get the bus around badly-parked cars.
One weekend I hired a car to go to a wedding with my wife, and without thinking I drove it (slowly) over a fairly high granite kerb while turning the car around in a cul-de-sac. Doing this destroyed the tyre. Car tyres are generally much tougher than bicycle tyres, but are smaller, narrower and more fragile than those used on a bus.
On one of my regular local trips I have a bridge crossing where I use the pavement (= sidewalk for US) rather than the road, as the road is narrow and separated by high concrete kerbs from the pavement. To get onto the pavement is easy, I use a ramp a few tens of metres from the bridge. At the other end there is a kerb with a drop of about 13 cm, so I stop, put my feet down, roll the front wheel off the kerb, then advance very slowly with my weight off the saddle to drop the rear wheel off as gently as possible.
I don't think I have ever tried to ride a bike up any significantly high kerb, anything over 2-3 cms I look for a ramp or stop and lift the front wheel and roll the rear wheel over with my weight off the bike. I have occasionally ridden off higher kerbs a few times when not paying attention, so far without ill effects.
Potholes are another risk. Where I live, these are very rare on urban roads. If riding on tracks and paths I either avoid deep potholes (and significantly sized sharp rocks) by riding around them, or I stop and push the bike if there isn't enough room. I have been caught out a few times, the only damage sustained on a full-sized bike was when I hit a pothole going down an otherwise very smooth mountain road at about 60 km/h with a full touring load, this dented the rear rim slightly. I am a bit more careful on fast descents nowadays.