Most vinyl warranties require a smoothe surface to mount to. And as Ron said, it adds to the look too. If there's no smooth surface, a warranty may be voided. Hence, thickness may not matter. But ask ...
As for foil or non-foil, it may be a problem if any of the walls get a lot of sun. IF the foil is facing outwards, AND you have a dark siding, the heat build-up may warp the siding. I have white siding with 3/8" foil-backed Celotex facing outwards. The white siding doesn't attract enough sun to heat it up. And 2 out of 4 walls get a LOT of sun. I used 3/8" because I wanted to tighten up the house a little more. I even taped the seams with Tyvek Tape. (About $2.50 a roll at either a Home Center or a Roofing/Siding place like Bass Supply.)
Before he gets to work, you might want to look into adding more exterior GFCI electrical outlets and spigots. He can put in the 'boxes' and 'bibs' now and you can cut the holes later. (Or, you can cut the holes now and 'plug' them until after he's finished siding.) I now have outlets on all 4 sides and faucets on 3 out of 4. (One of the outlets was split so the bottom half works via an interior switch for the Holiday Lights.) Other than that, not much else to add. My best to ya and hope this helps.
PS: This is a good time to caulk up any visible 'cracks' at the corners and around windows since you won't have access to them any more.