What size pipe should I use?

The forge is a side blast, but not gonna do a water cooled tuyver on this forge till i build a more permanent forge, so It'll be consumed I know, but anyway.

Going to use a hairdryer for air supply

Whatever you can get your hands on. I've used 1" and under with side-blast forges (charcoal and smithing coke) and works just fine. I wouldn't use any smaller than 3/4" if I had a choice though. Bigger is better (to an extent) because it offers less reistance to the air blower, though this can be helped by giving it a smooth transition (from one size/shape of tube to another, e.g. from hair dryer to pipe). You could for instance modify a plastic funnel or the top of a 2 liter bottle.