Get the mgr to sign you up with HMA training as soon as you can, their online stuff is good. A Streamlight Stinger led flashlight is a good investment, if you spot leaks and worn parts for the techs to upsell, you will be their best friend. Have them show you what to look for. Get torquesticks for the lugnuts, maybe an inexpensive 1/2" torquewrench, if you get in the habit from the start, it's easier and those Techwrenches are too fragile for day to day lugnut use. Keep your work area and yourself clean, use floormats, no one wants a greasemonkey leaving grime all over thier car. Keep a rag and some window cleaner handy, if you get greasy hand or footprints on something, clean it up. Watch the sill plate and driver's door trim for marks from your shoes as you get in and out, even if you didn't make the mark, clean it, you will get blamed for it anyway. If the shop has rubber gloves, use them, take them off before getting into the customer's car. If you screw up, tell someone, it's a lot easier to fix before the customer gets in the mgr's office. You should do fine.
As far as moving the box goes, rent a small trailer or put it in the back of your truck, the shop will have a forklift to get it out of the truck in one piece, you can pull all the drawers to get it in there, use plenty of tiedowns and furniture pads,