I don't know if those tires are manufactured to handle 60 psi. they must have some sort of max pressure on the sidewall perhaps it is a metric measurements "KPA" or"BAR" on the sidewall that would need to be converted PSI equivalents. Some simple tire air gauges have multi-type presssure readings. Check the tire for a KPA or BAR inflation number.You are most likely safe at 50 PSI.
That bike was stored well looks to be in great preserved shape, but hubs & Headset, the bottom bracket all need lubrication.
These should be oiled sooner than later if you need to use this for 8 mile rides to work. The hubs are easy to oil The headset can be oiled flipping the bike over.
You can get oil down to the crank through the seat post tube.
These are only temporary lubrication band-aids and these components all need dissasembly-cleaning & fresh grease when re assembled.
Then you can search for YouTube videos to restore the grease hubs & other individual components for your Raleigh.