Question about tumbler

I want to purchase a tumbler to strengthen some of my work. I was wondering what tumbler you use and what a good capacity size would be. Also, do I need two different solutions for polishing and strengthening?

You don't really use a "solution" for polishing and strengthening. Instead, when you put the silver piece in a tumbler with steel shot (tiny pellets made of steel), the natural friction of the pellets against the piece polishes and hardens the silver. You should also add a dab of dawn detergent to clean the piece as well and cover everything with water (just an inch higher).
The final shininess is determined by how much time you leave the piece tumbling, normally between 1 and 2 hours.
I personally have a Lortone 3 pound single barrel, which I really like. Connie Fox's site sells it for a reasonable price. She also sells bags of steel shot, you should get a couple of pounds.