TarnX works great on cleaning stubborn silver, gets right in the creases and everything. It can be found at Walmart, and I'm sure online too!
Prolonged cleaning with creams and paste will wear the plate away (assuming you have plate and not solid). The liquid dip type stuff will be less work and be far better for long term care.
If it is good, sterling silver, would not use the tarnX or other liquid dip. It will remove a desirable patina from the grooves and patterns. A good silver polish and some elbow grease is better for the silver.
Then once it's polished, you can keep it that way by getting silver cloth by the yard and making bags to store it without tarnishing.
Of course, this is just why I got rid of my silver. I felt like it owned me LOL. I didn't love it really, and didn't use it except for some everyday flatware I do enjoy using. If you use it with regular washing it doesn't tarnish.
A tip from silversmiths: a glass baking dish with aluminum foil. Place pieces on the foil in the baking dish; keep one spoon out. Sprinkle 1/4 to 1/3 cup of baking soda over your pieces. Pour very hot or boiling water over the pieces; it will bubble. Add a few drops of Dawn. Use the spoon you kept out to stir to dissolve the baking soda, then put that spoon in the baking dish with the rest. Or, use a wooden spoon to stir. Allow to cool, about 20 minutes. Rinse with water, dry & polish with soft cloth. I use this to clean tarnish from sterling silver. Heavy tarnish might need a second application. The best part is that, once you wash the baking dish, it can be used for food- no poisonous substances!