I always had good luck with just a compost pile. 3’ circle of fencing and just keep piling on as I get stuff. In the fall get the wheelbarrow out, skim the topmost stuff (uncomposted) off to the side and spread everything lower on the garden then pile it all back up. I had my best luck spreading it in the fall. Winter, nothing is going to really work in a small household compost, too cold. By tilling it in the fall, the organism’s do their thing when weather permits.
I am a big fan of newspaper and cardboard. Peanut shells also. I accumulated newspapers (back when I actually got and read them) then spend winter evenings ripping them into 1” strips. Peanut shells just grind them between my fingers as I shell them and accumulate in paper bags. I love me some fresh roasted peanuts and would by them raw by the 25# sack. Spread in the fall then till in. Good to go for spring planting.
My last technique before I left the place, was to dig scraps right into the garden. I would always have a section fallow and just take a shovel of dirt up, toss fresh scraps in then put the dirt back in the small hole. Move where you dig the hole a little each time down a row. It was working very well for the small kitchen container of vegie scraps.
Now, I have tried using newsprint for mulch. Put a layer of 3 or 4 strips down and cover with mulch (triple shredded hardwood mulch was my go-to). The newsprint never seemed to let enough water through. It worked better if I crinkled them up as I spread but that was too much work. I ended up being happy spreading them in the general pile.
My black lab LOVED to help with shredding. Her job was cardboard boxes. I would giver her one and instruct her to “Compost it.” She would go to town ripping the box apart. Point her to a piece and say “That’s too big”, she would rip it apart more. Kept her busy for 30 minutes a box… “That one is too big… That one is too big… Too big, too big, too big…” Not too messy of an operation. Ended up with a sweepable pile in the living room and a very, very happy lab.
As far as care of it? I would stir/turn it now and again, water when it was dry and they pretty much take care of themselves. I have read about percentages of green to brown, but never paid it much mind as what I got from the yard and kitchen along with the paper always seemed to compost well.