Here's the official website for all the transport links etc. on this trip:
http://www.alpen-route.com/

There's a tonne of information in Japanese only on the FAQ:
http://www.alpen-route.com/inf1-inquiry.html#

I'm putting ome snippets from the FAQ here in English to answer your questions (and maybe raise a host more):

Foliage
The foliage will turn to Autumn colours roughly:
Mid-September: at altitudes over 3000m
Late-September: around Murodo Daira / Daikanbo / Danbo Daira
Early October: around Midagahara
Mid October: around Kurobe Dam / Ogizawa
Late-October: around Bijodaira / Hyugasan Kogen
Early-November: around Tateyama station

With so much gorgeous foliage, you can be pretty sure that mid-October is going to be a very popular time to visit this area. So make your reservations in advance - and (if possible) travel on a weekday rather than a weekend to avoid crowds.

Clothes to wear:
http://www.alpen-route.com/bsc2-accout.html

Left Luggage Facilities
In all stations along the route there are coin lockers for hand luggage. If there are no available coin lockers, the station office can hold your luggage for a time.

There is also a luggage delivery service. If you are staying at hotels on either side of the route, you can have your bags delivered from the first hotel to the other side - whilst you make the trip over the hills with your hands free:
The following is a list of the hotels that can do this for you:
http://www.alpen-route.com/bsc2-recomm3.html


Final note - I've seen this journey in guidebooks etc. but always figured that the whole chebang was set up in order to showcase the Japanese river-damming and concreting industry (Kurobe dam is some kind of national monument to the power of Japanese construction over the forces nature). But maybe I'm missing out on a wonderful trip through the mountains on some really cool trains and things... please post a trip report here and let us know if it's a worthwhile trip.