Ozarksgardener - welcome to the forum.
If you want to give the tumbler a try don't worry about the rust. Start loading it up. Hopefully the tumbler has lots of holes in it for air circulation. If not you will end up with a sloppy, smelly mess instead of compost.
Don't worry about drying your kitchen scraps - just toss them in. Make use of your coffee grounds, filters, tea bags and crushed egg shells. Add a handful of garden soil to get some microbes in the mix and add some browns - mulched leaves, shredded newspaper (black and white only), shredded toilet paper and paper towel tubes. If you use shred news paper add a little at a time so you don't end up with messy wads of paper.
Since I dump my kitchen scraps daily I don't need a large container on the counter. It is a plastic container, probably 1/2 gallon.
If you want a larger container and don't have a kitty litter or laundry detergent bucket visit the fast food joints. They get their sliced pickles in 5 gallon buckets. DQ also gets frozen strawberries in 5 gallon buckets. They are sturdy, have a snap on lid, a good handle and can be gotten for little or nothing. I have found many uses for those buckets.
When I first attempted composting I just piled up leaves and grass clippings. It was Okay but not the best. It was kind of an eye sore, it was a pain to turn and I did not have a good balance of browns and greens.
I now have 2 4' x 4' x 4' boxes made from scrap lumber and chicken wire. They are adjacent to each other to make tossing easier. I find it much easier to toss from bin to bin rather than turning one bin. I do not have critter problems so the tops are open and the front of the boxes is mostly open with an 18" footer to keep the compost in the box. The open front makes tossing and removing for use very easy. My neighbor wanted compost bins but did not have scrap lumber. She scrounged around and got her hands on wood pallets. She screwed them together to create the sides and backs. G cut down a pallet so she could have a footer on the front.
In prior years I had no problem collecting browns. We had an enormous live oak in the yard. Last fall we had to have it removed.
The branches were splitting from their own weight and were a danger to G's shop, the patio and the house. I will have to get creative for my browns. For now I will have to rely on shredded paper and tubes. In the fall I can collect bags of leaves left curbside in the neighborhood before they are picked up by the yard waste service.
Caution: once you find a composting system that you are comfortable with you will be hooked for life!
Do check out the stickies on composting. Great information especially for a beginner.