Trains are not (yet) a viable method of transportation from Ben Gurion int'l airport to Jerusalem, that is why I completely ignored them when writing the transportation section. They are the best method to get to most parts of the country, except Jerusalem (until 2018, see footnote).
Here are some of the main reasons trains are not (yet) a viable and comfortable method of getting from TLV to Jerusalem:
1) Train service from Tel Aviv to Jerusalem is somewhat infrequent. It runs every 60-120 minutes only between 05:51-19:51.
Typically, passengers take transportation immediately upon arrival, the chance that it would be synchronized with the train to Jerusalem is not high. If the passengers will not check the schedule, they may wait in Tel Aviv for a train to Jerusalem for an hour, or worse - get there when no trains to Jerusalem run until tomorrow.
2) Even when you are taking a train to Tel Aviv that leaves you the minimum wait time (34 minutes, which is already a lot) the overall duration of the train ride is mostly over 2 hours (!!!, driving takes only 40 minutes).
3) You get to Malha train station, which is situated very far from the city center with 2 infrequent bus routes Taking a bus to your destination will mostly be by taking 2 buses (tourists will probably have little idea where to switch buses).
Taking a taxi from the train station will cost in average 40-50 NIS. Add to that the train ticket fare - the airport shuttle is cheaper.
Add the time you would be spending in Jerusalem (buses / taxi), the overall duration is about 2.5 hours (if everything is smooth...).
4) The train doesn't run from Friday noon to Saturday night.
For all of the reason above (taking a lengthy ride that puts you in the outskirts of the city, infrequent service), the airport shuttle is much more viable (shorter ride, takes you directly in your address of choice in Jerusalem, runs 24/7).
When the new train line to Jerusalem will be finished in 2018, the train from the airport to Jerusalem will take about 20 minutes, and in Jerusalem you would be able to easily transfer to tram (the tram stop is right outside the new train station) or bus (over two-dozen bus routes go through the new train station perimeter!), but until then, train is definitely the least viable transportation solution to Jerusalem.