Yep, you shouldn't rinse your mouth, because a proper toothpaste has fluoride, which helps remineralize enamel. Keep in mind it won't restore already decayed enamel though.

Anyway, I am not that sure about electric toothbrushes. At least it's not necessary. On Wednesday when I've been on dental check-up, I asked my dentist whether electric toothbrush would be a good idea. She said "Well... it can be... but you already do pretty good job of cleaning your teeth, so I just recommend you stick to that." I just use a regular toothbrush. However, just the brushing does take me a while. About 10-12 minutes. Yeah.

Well, something that could be a tip is xylitol chewing gum. Most sugar-free gums use xylitol. It is artificial sweetener that's actually good for teeth. It helps remineralize teeth like fluoride, remove plaque build up, and it kills acid-producing bacteria. That is because the bacteria consumes it like regular sugar, but it can't process it, so it just dies. You can also buy xylitol as a powder, because it's, well, a sweetener.

Now to the disadvantages of xylitol: Consuming larger amounts (I think it's just around 25g) can cause diarrhea and cramps. It is also extremely toxic to dogs. Just 100mg/1kg can cause them seizures and 500mg/1kg can cause death. Obviously that's just approximate, so keep your dog away from xylitol.

Disclaimer: I am not a professional in this field.