Well, I'm looking at Zaino's site while pondering your question.
Zaino's Z-Kit I is a very good kit to start with. It has everything you need, and the quantities will last you an entire season. The only addition would be to order an additional bottle or two of the car wash.
Also, if you have leather, I highly recommend Z-9 leather cleaner, and Z-10 leather conditioner.
For drying and polish removal, I'd suggest the "blonde towels". A 3-pk would be the minimum (2 for drying/1 for polish removal), but I'd recommend ordering 2 3-pks.
I use sheepskin wash mitts for washing, which can be found at better automotive stores.
Some "over the counter" products I've also used in detailing are;
Turtle Wax Ice Total Interior (for dash/inner door/etc., maintenance)
Armor All (spray not gel) for tires
* Some opinions are not favorable towards A.A., but its always worked well for me*
Stoners Invisible Glass (not aerosol can-use spray bottle)
Stoners Tarminator
If I think of more, I'll let you know, but that covers the basics.
Ed