I've painted many rims.
1: not for bikes with rim brakes.
2: easier if you remove the spokes.
3: some colors are much easier to work with. (silver is awful).
paint doesn't stick to chrome very well.
if chrome is flaking off, I'd say file them in the recycle bin.
aluminum rims are lighter weight and will make the bike ride better.
will all the work needed, stainless steel spokes always look better and will match up better than some old crusty zinc plated spokes.
a light/translucent color will show all the defects in the rim.
that rim look like it's aluminum. The brown spots will just clean off as aluminum doesn't rust. Maybe it was parked near a grinder and all the metal bits landed on it and rusted.
I think a gold lacquer would get the look. go slow. Apply very lightly. Let the clean metal shine through.
Fuji used gold anodized rims on certain models of 10 speeds long ago. The brakes wore the yellow off the sides. ugh. There were gold bmx rims in the 1980s along with red and blue. I've seen a number of 1980s/1990s department store bikes with yellow lacquer over chromed steel. It's mostly faded/pealed off by now.
There are also home anodizing kits. Never tried it. Eastwood sells kits. DIY vids on youtube.