A 96 quart Sterlite would be great! I would say the sides need to be 12 - 18 inches high. And be sure he can't climb on top of his Igloo then escape over the side that way (just put the igloo a little ways from the side). You're right - you don't want something too shallow.
FYI, there are cages online that you can buy too...or you can buy a wire cage (similar to ferret cages) but the Sterlites are the most popular, practical & affordable.
We actually have a ramp/ladder toy for Louie but we put it in the middle so he can't climb up & out.
For bedding I use Cellsorb Plus and it works great. I would HIGHLY recommend this. It's amazing stuff. http://www.cell-sorb-plus.com/
Most hedgie owners use this stuff and swear by it.
If you're going to potty train your hedgie you can use bedding in the litter box but use a liner (like Cait* does) for the rest of the cage. When we were trying to potty train Louie I used a liner - but we can talk about that later...
Pine bedding is ok (it has to be Kiln dried though) but one problem with shavings and hedgies is that it can stick to them and get carried around your house! LOL
I've actually heard that corn-cob bedding is NOT something you should use for hedgies! It's gets moldy quickly, they may try to eat it (which can be a hazard), it can be harder for them to walk on, doesn't really encourage burrowing or nesting and can get "stuck" to ummm, some personal areas. I don't know why that pet store is using it - they should know better - but you will want to stay away from it!!
I'm gonna use another reply for the food issue....