Drill size for thermal via (and how many)
For hand soldering, one (or two) large holes are best as that way you can ensure that there is a good solder joint between the PCB and the thermal pad. Unless you use reflow techniques, there is no other way to ensure a good connection, and leaving the pad unsoldered can lead to poor thermal performance - think air between the chip and pad.

For production, lots of small holes are better, as you said, more area between the top and the bottom. In fact many datasheets will have recommended layouts for thermal pads which usually show lots of small holes.

What I do when hand soldering a board is usually have one large hole (as big as feasible) in the centre of the chip, and then several small vias either side to increase the amount of copper between the top and bottom. You can then feed solder into the large hole after soldering the chip on - put the soldering iron tip in the hole and then feed in the solder. This should achieve a good solder joint to the pad.

You can also add more holes either side of the chip with a large plane connecting them if more heat transfer is required.

One thing to remember though, make sure that thermals are off on the section of copper plane that is connecting these holes. Adding thermals to the vias/pads being used for heat transfer will only reduce thermal conductivity.