I love gear questions, for some weird reason!
Ok, I will answer this since I'm a big fan of changing tables. Re. orientation, definitely baby laying sideways to you. I have a hard time changing diapers while facing baby perpendicular. It may be just what I'm used to though.
Supplies- my table has a large drawer right underneath the part where baby lays. Then there are 2 shelves under that. In my drawer are extra changing pad covers, also piddle pads. These are waterproof pads that are invaluable when babe is really young. I would always put them under (at least their bottom area) so that when you are changing them and they pee or poop (and they will), it will go on pad and not cover, so that you're not changing that all the time. I cloth diaper so I have various supplies in the drawer... extra snappies, diaper creams, lotion, extra diaper pail wet bag, nail clippers, etc. On the shelves I have matching baskets. In one is extra cloth wipes and face cloths, in another is burp cloths, in another are my prefold cloth diapers, and in another are my diaper covers/liners. I also keep a spare package of disposables and disposable wipes on bottom shelf, and a container of cloth wipes on the upper shelf.
The changing pad I have is concave the length of the pad. I like this pad just fine.
You'll find exactly what you need/want for this area, but this is the jist of what's helpful. I don't keep anything on the actual changing pad, except maybe a toy sometimes, dd3 is 15 months and super squirmy, so a toy is a helpful distraction.