A few questions:
How much of a performance benefit am I going to get with .20 over or .40 over pistons/rings?
Slight improvement there but I think you're going to have a hard time finding 0.020" or 0.040" overbore pistons for your application. Mainly because of the smaller wrist pin you have in the 1.3, Si pistons can't be used unless you go custom (about $450 or higher). You could get by using a standard 1.3 overbore piston but good luck finding anything other than 0.5mm (0.020") oversize. With the low mileage your engine has I'd recommend using the original ones if they're in good shape and hone the cylinders.
The 1.5 gaskets and such will fit my 1.3, right?
Absolutely, and if you're not going to use Honda ones I always go to my local NAPA store too. Even the head gasket the 1.3 & 1.5 have the same bore.
I believe my engine comes with a crank that has slightly smaller journals, would undersized (thicker) bearings compensate for this, or should I get ones specifically for this engine?
Nope, not even close. you have to get the ones for your engine.
Jay