What kind of maintenance should be performed daily, weekly, and monthly?
Furthermore, what products would be best for things such as cleaning?
A comprehensive list may be difficult for my tired brain, but here's a start.
Tune the instrument. At least test it every time you take it out. Don't defile yourself and others by playing an out-of-tune violin!
Rosin the bow by rubbing your rosin cake up and down the length of the bow several times, and the gently wiping the excess rosin off with a soft cloth.
Wipe rosin dust off of the varnished wood of your violin with a micro fiber cloth. This protects the varnish.
As I think of more, I will edit to add them. I believe this is a valid question because there really is an exhaustive list, at least of things I do daily/weekly/yearly, so there's no "infinite loop" problem.