As a Periodontist, I get asked about recommendations for toothpaste all the time. What most people dont know is that plaque is removed by the mechanical action of the toothbrush bristles against the teeth and gum whether toothpaste is used or not. Much to the toothpaste manufacturers chagrin they have never been able to prove that using toothpaste increases plaque removal, it simply makes for a better experience by adding some flavor, thus the title.
Here are some guidelines to consider:
Always use a fluoride toothpaste.
Some toothpastes contain different additives for different functions, such as whitening and or tartar control agents. These work with varying degrees of success, most will only notice a mild improvement. Tartar control toothpastes can lead to increased tooth root sensitivity, so their use should be avoided by periodontal patients.
Sensitivity toothpastes are helpful after periodontal procedures and for people with tooth root sensitivity.
Baking soda alone is a good toothpaste, but doesn't have fluoride. If you are in an area with fluoridated water that may suffice. Baking soda should not be used with salt water, it is too abrasive in that formulation. Baking soda should not be used with hydrogen peroxide on a long term basis and ideally that should be prescribed and monitored by a dental professional.
In conclusion since toothpaste does not play a significant role in plaque removal use whatever you'd like but strive for one with fluoride. Always use a soft toothbrush. Medium or hard toothbrushes are too abrasive.