Best, simplest, cheapest way to start compost... in a neighborhood?

Over 18 years ago, I landed in a small 1990's build cookie cutter neighborhood of starter homes, and I can't move right now. My backyard is 1/2 acre, so we have some space to work with. But I would still like to be as little of a nuisance to my neighbors as possible. The side that sees most of my activity doesn't necessarily care, but the wife is particular about her produce, so they can't always be "bought," so to speak.

Anyway, all that context to say I do have to be mindful of how I operate as opposed to if I only had to worry about impacts to nature. I also can't and don't want to just buy those tumbling things from Amazon.

I'll try to add a drawing in the comments at some point, but the backyard is a little over 100 feet wide, runs north to south, and is 300' long on the west side, shorter on the east. There's a gentle slope north to south, as well. I have no idea about degree. Enough that water runs into my neighbor's yard. Zone 8a, if that matters for composting.

We back up to woods and also have dogs. Unfortunately, all the currently dog-proof areas are closer to those neighbors.

In short, I'd probably just start a heap somewhere if I didn't have to worry about neighbors, but I do. Any advice is appreciated! I'll start working on a drawing (I know, I should have had one drawn like 16 years ago!).

ETA: My primary goal is waste reduction, not necessarily the fastest path to useable compost. Our soil is pretty good, and I use "chicken dirt" in the spring to top dress my rows. Basically we rake back the mulch and scoop out all the pretty black dirt, then add more mulch.

For myself, I have found the best system to keep friendly with the neighbors is through the style of a big pile covered with natural brown materials.

My pile right now is covered in a mixture of autumn leaves and old straw. When I add contents, I will pull back the covering with a pitchfork and add the new contents near the core before covering it back up. I don't have a container around it but have considered making a pallet-based box just to keep up appearances. My mound is located near my trees away from the houses so it generally isn't noticed. While the placement isn't close to the house making it bit more of a chore to add to the pile, it keeps the peace so I tolerate the walk.

In a situation with neighbours, I had a lot of success with a 36" tall dog exercise pen formed into a circle, and kept covered. You can pick them up inexpensively used. I liked how portable the exercise pen was and it looked tidier than just a heap or my attempts to make circles with wire fencing, and the volume it contains is about right down a pile.  I operate my piles as 1-2 year cold compost piles, with each year getting a new pile, and ideally, the pile sitting another year before use.

If one is inclined to flip their piles, the ex pens open up easily to allow you to do that, but I decided the increase in speed want worth the increase in work to me!

Of course, keeping the pile covered with carbon rich materials to avoid smells is important too.

In my experience dogs love to scavenge in compost heaps. mine love vegetable peelings and aren't fussy where they get them from. Other critters will as well - birds and rats in my case are the problems, slugs and mice just turn the heap and eccelerate the breakdown. If you just compost garden waste (leaves, grass clippings, weeds..) then you're less likely to have a vermin problem, although it would be a pity to lose the nutrients in the kitchen waste perhaps. I tend to just chuck the garden waste in a pile out of the way to break down, and use my compost bin for the kitchen waste (along with some sawdust for added 'browns). A covered pallet cube is an easy way of containing the pile, but you may need to consider something like hardware cloth, or metal sheeting if rats are likely to be a problem.

They say a compost heap needs to be about a meter across to have a core area big enough for composting (so a half-meter of thickness all around to insulate and keep in the heat). A round footprint is good because you get that half-meter of thickness all around  - harder to generate heat in the corners of a square heap. The corollary is that it also needs to be a meter tall or more - and that would be a LOT of kitchen scraps; perhaps more than I have made in my whole short 65 years (considering that they are perishable). To make a working heap, you kinda have to start with a big pile of organic like yard waste and add in your kitchen scraps on the fly.

A heap needs turning, because of the differential composting action between the center and the edge, but you don't want to move the whole pile! I have found that making it work like a silo is somewhat effective. You need a tunnel into the center at the bottom and a long-handle shovel - you can excavate it into the heap but that can be tough digging based on my prior experience; if I started again, I would make a bridge so I could dig from the center without the heap collapsing on the near side; maybe made from some scrap plywood set into an A-shape so I could get the shovel to the center and the pile could settle centerward. Then it is possible to dig out some finished compost and use it as cover over the newest kitchen waste - and also keep adding yard waste as it becomes available. Whenever you dig from the bottom, you should be getting finished material for whatever uses required. But sometimes I have dug out a whole rotten onion or broccoli stem or such; have to sift that out and put it back on top to try again.