I won't enter the debate of car wash vs. hand wash, but if you move forward with the $10 unlimited I would recommend the following Adam's products for home use. Basic, easy to use, and quality...
Exterior:
1. Good microfiber cloths (
click)
2. Detail spray (
click) - I go to a self car wash and then use the detail spray when I get home to remove any soap residue/spots or hit areas a missed a bit
3. Ceramic boost (
click) - Meant to augment a ceramic coating, but I use it occasionally after detail spray even on my vehicles without ceramic coating and it creates a nice smooth, hydrophobic surface
4. Pick a glass cleaner of your choice
Interior:
1. Interior detailer (
click) - Literally use this on all surfaces on the inside of my vehicles to keep them clean/fresh. I'll use more/other products every six months or so to do a better job, but love the interior detailer.