When going to Jerusalem from the airport, I generally stick with the taxi and "splurge" for the convenience. Cost would be around NIS 250, though they will generally take USD.
Sherut is NIS 62 and can't be ordered in advance. Drivers will vary on whether or not they take USD. There is place for luggage in the sherut (shared taxi), known as Nesher.

Regarding bus, you would need to take the shuttle bus to Tzomet EL AL, and then take the 947 from there to Jerusalem Central Bus Station, and then take a taxi, city bus, or light rail to your final destination, so public transportation isn't your best option.