What PSI would you keep it at?

In a perfect world with roads as smooth as glass, maximum inflation would be best. The world is not perfect & neither are roads. And everyone weighs a different amount.

Minimum inflation (even with a lighter rider) can result in pinch flats where the rim of the wheel crashes down upon the tire & tube, creating "snake bite" like punctures. Maximum inflation can cause anyone on rough surfaces to bounce across bumps or through a pot hole...losing contact with the road.

Experimentation is the key. Start near max inflation & go for a spin. If it's too rough, drop a pound or two out. But never go so far as minimum inflation. Even a chunky guy (like me) doesn't run max inflation on rough city streets. On a bike with tires going to 125 psi, I usually run around 110 in the front & 115 to maybe 120 rear.

There will be slightly more weight on the rear wheel, so you could have the rear tyre at a higher pressure than the front.

For riding on smooth roads it's usually better to have the tyres close to their maximum pressure, but if the roads are rough you might want to run them at a slightly lower pressure. You need to be careful though, running them at too low a pressure will give more potential for pinch flats if you hit a pot hole or object in the road, so do not go below the minimum recommendation.

With the tyres that you have I'd try something like 100 - 110 psi in the front and 125 - 140 in the rear.

The pressure has to be in the range printed on the tire. Where you keep it has to do with rider weight, cross sections width, and type of riding.

On road riding 700x20 racing tires I keep both front and back at max 125psi (max 125)

On road riding 700x23 training tires I keep the front at 110 and back at 120 (max 125)

On road riding 700x21 tubular tires they are at 190 rear 180 front (max 210)

On road riding 700x32 cross tires 95 rear 90 front (115 max)

Off road riding 700x35 knobies 75 rear 65 front (90 max)

That's all I have to use for personal example.

I keep the rear tire a bit higher because they carry more weight. The exception is the racing. I tend to be leaning more forward being down in the drops more and standing a lot when sprinting.

It will depend on your weight and the size of the tire. Start at max and go for a ride. If the ride is too harsh drop it a few pounds. A lighter rider will get the same ride as someone heavier but at a lower pressure.

a. put the higher one on back

depends on your weight

100 is plenty for up to 200 lbs usually

145 will be so hard you won;t want to ride it really

what kind of tire is that, why are they so different?

one sounds like a hybrid/fat tire, and the other like some super skinny tubular racing tire

wle