OEM pads are pretty good, there's lots of others. I'm sure autoparts stores sell good ones alongside junk ones... Search, there's probably lots of threads arguing about what kind is better than the others.

Just compress the piston into the caliper. The reason for opening the bleed screw is so you don't push too much fluid back into the reservoir & overflow. Open the bleeder a little while you're pushing the piston, close it before you quit pushing. That way you don't let air in.

I know you said you don't want to bleed the brakes, but this is a good excuse to bleed fresh fluid thru the whole system. It picks up moisture from the air & that makes it corrosive.

I don't like to ever pinch the hose, & never let the weight of the caliper hang on the hose. I've had a hose burst while stopped for a train & I didn't like the feeling...

The trick for the rear is twist the pistons, don't just push them in. That's because of the handbrake auto-adjusting mechanism.

Make sure the caliper slide pins are greased & they slide smoothly. Make sure the new pads fit nice into the caliper brackets. Sometimes I have to file the paint off their ends so they don't wedge too tightly. Little grease or anti-seize is good where they move.