This seems unnecessary to some people, because they never had to do this with their last few dogs. But, our knowledge constantly evolves.
Dental health ties directly into the overall health of the animal. Gum disease in dogs, like in people, increases the risk of heart failure an other issues.
If your dog has a lot of tartar and plaque buildup, tooth brushing alone won't cut it. They really should have a full dental cleaning under anesthesia. Unlike people, you can't just tell a dog, "open wide" and expect them to do it and hold still. Performing the dentistry under anesthesia is the best way to do a really thorough cleaning.
At the price that was quoted to you, it sounds like a nice routine dental. If you choose to wait, you run the risk of increasing the buildup, and beginning gum disease. I've seen people balk at the price of a routine cleaning, but then a few years down the road, now the dog's teeth are rotting, they might have a tooth root abscess or they need extractions. The price for this will be SIGNIFICANTLY higher.
Once the cleaning is done, tooth brushing is the best option to keep the teeth healthy. You want an enzymatic toothpaste made for dogs. There are other options (a liquid you can squirt onto the teeth or put in water, chews with the enzymes on them) but they are not as effective.
If you are worried about your pet having anesthesia, you can do pre-anesthetic bloodwork. This panel will check the function of the internal organs to make sure they appear to be functioning properly. That said, anesthesia is always a risk, but not addressing dental care ALSO puts your pet at risk.
