Well minu, you are very lucky that you have the city compost, so you have organic compost available and a way to deal with your own garbage so that it gets used instead of polluting the water supply. So you do have the option of not composting yourself, which most of us don't.
But doing your own compost is free, easy, and very rewarding. It always seems to me like participating in a miracle to take my smelly icky garbage out to the pile and watch it become rich crumbly dirt.
A compost "bin" can be anything (lots of materials available on freecycle) you have on hand. Concrete blocks, wood, wire. Mine is a grid of wire bars that I bought for $30 about a decade ago and am still using.
I do very little work at composting. I save my kitchen scraps in a tightly closed bucket under the sink. Once a week or so (a little more in summer, sometimes less in winter), I take the bucket out to the the pile and empty it, clean it out and bring in a fresh one (they are kitty litter buckets and I have several so I can rotate them). When I dump the kitchen scraps, I cover them with a big layer of weeds, leaves, whatever organic material I have on hand. If it's dry enough to water my garden, I water the pile also. That's it.
I don't turn the pile or do anything to it. 3 times a year when I want to use the finished compost, I turn the pile over. That is I take the stuff off the top to become the bottom of a new pile. When I get down to where the earthworms have collected, I stir that around a little and anything that isn't already finished compost rapidly becomes so.
My bin is about 3'X 3'. When I turn the pile over, I start the new one right next to it (and move the bin to cover the new pile), so my whole composting area takes up 6X3.
Is there any down side? Other than the small amount of work I just described, the only thing I can think of is that small critters do come to it sometimes. My wire grid (including over the top) is small enough openings to keep out the raccoons and possums, but not the mice/ shrews or whatever. I don't know that it is attracting them, they are here in the neighborhood anyway. The pile is far enough from the house (maybe 40 ft) that I don't feel like I am attracting anything TO my house. It is visible from the deck, but is not an eyesore, mostly looks like a pile of leaves. You never see or smell garbage.
What would be the advantage to you since you have the city compost? Other than the satisfaction of participating in it, I guess just to have your own compost sitting there waiting for you whenever you want it.