Whether you might have unwanted critters, opossums, raccoons, etc., digging in your compost depends on many things, mostly just where the scraps from the kitchen go. If those scraps are simply piled on top of the compost pile they are readily available to those critters, but if they are buried those scraps will be more difficult to access.
Some times I have had these critters dig in my compost but mostly not.

Here is a link that might be useful: Composting Tutorial

Cheapest critter proof bin is a circle of chicken wire, as wide as you want. Lay a chicken wire lid over the top and attach with a few twisty ties. If they dig underneath, you can put chicken wire on the ground first.

When it's full, unwire the cylinder and set it up next to the pile. Fork the top layers back in until you get to finished compost.

This is the simplest way I can think of.

Consider 'trench composting" ... dig a trench between rows in the vegetable garden and bury the scraps in it.

Next year, shift the rows so the seeds go on top of the scraps.

I have seen both Opossums and Raccoons climb chicken wire fencing and the mesh allows thingys like mice to get in with very little effort on their part.
Unless the material is buried quite deeply, I have also seen these critters dig up to be composted material put into trenches, and that depth is below a plants normal root zone.

I use a trash bin but I don't roll it around. I work it through with a shovel or pitch fork. It may not be as effective but I think one thing about compost is true: it will all break down, just depends on how fast you want it to do that.

But you can also try vermicomposting (worm composting). You can do that inside your home in a relatively small space. Using similar food and other wastes like a compost bin, but you are feeding the worms and using their castings, instead of using the decomposing compost material.