You must keep in mind that the toothpaste is cosmetic stuff after all, and that the toothpaste cannot clean the teeth itself.
Here are some of the mistakes that you do while using a toothpaste:
You use it too much
If you use your toothpaste in an amount that is almost like pea-sized, it will still taste good.
You are not brushing your teeth enough
You need to brush your teeth for at least two minutes, because you will certainly miss some places.
You do not pay attention on the way you are brushing your teeth
Make sure that you do not miss any places, and brush each place for two minutes.
Do not forget that brushing is what cleans your teeth and not the toothpaste. If you want to get rid of plaque, all you need to do is brush your teeth. There is no mouth wash, toothpaste or gel that can make a big difference.
Therefore you can use any toothpaste. Choose the one that tastes good and gives you a sense of purity.
Also, you can use baking soda, or coconut oil. You just need a good technique and you need to brush your teeth quite often.