One thing to keep in mind for the wheel is that on 360 degree games there is no center, so you do not want a wheel that gives any impression of which way it should be held to be centered.
If not trying to find a used arcade one and you have the means to fabricate the shaft, what you are probably going to want is a 10" three spoke go-kart steering wheel. Make sure the spokes are evenly spaced.
It has just a little bit more weight than an original arcade wheel, but the size and appearance are perfect IMO.
https://www.amazon.com/Maxpower-5890-10-Inch-Steering-Go-karts/dp/B005FMT2RA (pic sucks, but the reviews have better pictures)
I don't remember what game it is from, but I bought an original used arcade setup without the wheel and it just used a bronze bushing. I'd probably go for bearings, but that is what the original used.
The original arcade mounting screws fit the pattern on this wheel.
There are also deeper 5" dish versions.
If you'd rather stick with lightweight plastic stuff, these playground wheels might work:
https://www.amazon.com/Playground-Steering-Wheel-Portable-Swingset/dp/B08KTJMTPG?th=1
Or if you're into 3D printing, print your own:
https://www.thingiverse.com/thing:5350668/files (scale to desired size. The print is for half a wheel. Print two and glue together.)
A wheel with a defined orientation isn't a deal breaker, but isn't optimal IMO.
The original pole position game had a wheel with a definite up and down despite the car resetting the center position every time and requiring you to hold the wheel at whatever angle it was at when you wrecked. That feels wrong to me, but that's how it was.
Long live Ivan Stewarts Super Offroad!