Here is the single-speed I built in 2011 using advice from this website and which until this month has been my sole bike.
Raleigh frame branded Triumph. Date uncertain, it came to me with a broken saddle, 2 somewhat buckled steel wheels and a Sturmey-Archer three speed that only worked in 3rd gear and was dated 1987. Bought it from the daughter of the guy who bought it new.
Current spec largely unchanged bar maintenance from how I built it 9 years ago, excepting that I removed the chainguard (chainline has changed, it no longer fitted) and both mudguards (they didn't work with the wider tyres)
Shimano UN54 bottom bracket
Raleigh singlespeed crankset
Blue steel BMX pedals and blue BMX chain
26x1&3/8 modern Raleigh alloy front wheel
Custom rear alloy wheel, 26x1&3/8 singlespeed (freewheel) with 22t cog
Original brake calipers. Modern pads. All new white brake cables
New white handlebar grips to replace black as fitted
Mountain bike brake levers to work with the modern-format brake cables. Both on right side as I have little strength in left arm due to an accident half a lifetime ago.
Modern plastic rear mudguard.. it isn't painted, I found it on eBay in Triumph blue and is an exact colour match.
New white saddle to replace brown leather broken one it had originally
Schwalbe Delta Cruisers (Not happy with these: the protection against puncture is good enough but they just don't last, I'm near the end of the tread on the 3rd set it's had in 9 years. At the next maintenance cycle it's getting Marathon Pluses fitted)