Although I have yet to try the train option to Bourg-Saint-Maurice ( I have only done the Fly/drive or drive all the way options since buying there several years ago) I can only back up what John has said really. From the station there is either the Taxi/Transfer bus option or to go to the funicular station ( luggage with wheels on will be very usefull) which is roughly about 5 - 8minutes walk away ( if you come out of the station and take the road that goes behind the station and not up the main road).
At the funicular station you can thn either buy your ski pass at the funicular sation ( this will have the funicular included in the price ,for as many trips as you wish while the ski pass is valid) or just pay to travel up on the funicular and pay for your pass in resort. As John says the taxi/bus transfer option will save the walk to the funicular but may take some time, also if you take the funicular option and are arriving in BsM late in the evening the funicular only runs until about 8.30pm ( it could be 9pm but not 100%)
If you are ok for the funicular once at the top the transfer buses ( which are free) are to the left just pass the train kiosk ( they are posted) where the funicular arrives at. The buses are marked on the sides as to where they travel to.
You have picked a good time to go as Les Arcs (along with almost all resorts) are having a great season ,I’m out there myself from 15th - 20th April for a last minute blast.
What John says about driving is also true, it may sound scary but in fact driving is pretty easy , and if you have someone to share the driving with it’s fine, all along the french motorway system are rest stops/toilets and seating areas which are named and have a prefix or “Aire” Aire du Glieres for example and thse are every 10 - 15 km or so.
For BsM/Les Arcs it’s also quite a staright forward drive , from Calais take the A26 and just follow the signs for Riems ,Troyes, Macon,Dijon,Lyon,Chambery,Albertville,Moutiers and Bourg-Saint-Maurice and then up to Les Acs.
I hope some of this helps and wish you all an enjoyable and safe trip to Les Arcs
All the best