Can you recommend a gentle but thorough tooth cleaning product?

ADA approved paste. Any over the counter Fluoride toothpaste approved by the ada should be both gentle and effective when used 2 to 3 times a day. I would recommend the simplest Fluoride toothpaste without a lot of extra ingredients. Some of the newer toothpastes such as crest prohealth contain so many ingredients that can irritate sensitive patients. Just use a name brand simple Fluoride toothpaste.
Sonicare electric . Sonicare electric toothbrush. I use one myself.