I have a 2-stage furnace and I want to connect the 24VAC from the humidifier to the thermostat connections on the control board. Since the control board has W1 and W2 connectors, which one should I use in conjunction with the C so the humidifier operates when the blower runs?
W1 should work
If you want the humidifier running whenever the heat's running, then using the W1 and C terminals on the thermostat connection should indeed work.
...but, I'd make sure there's a humidistat on this
However, I would make sure there's a humidistat controlling the humidifier (it can simply be in series between W1 and the humidifier, provided it's an open-on-rise/close-on-fall type) as well, as too much humidity is a rather effective way to slow-kill a house.
The fact that you have a 2 stage furnace is less important in regards to your humidifier then if you have a 2 stage thermostat. The W1 are W2 terminals on the furnace are input only. They wait for a 24v signal. So if you have a single stage thermostat connected to W1 the furnace will kick in to 2nd stage after a pre-determined amount of time. Connecting to W1 would apply here. With a 2 stage thermostat the W1 contact is usually maintained during a call for second stage heat by the thermostat, so connecting to W1 still applies here. Sometimes I've run into a 2 stage with only a W2 connection at the furnace. Making it an expensive single stage furnace. In that odd case connecting it to W2 is the appropriate action. Or you could just wire the transformer into the HUM terminal.