I would put new grease & bearings in the hubs, bottom bracket & headset. It probably needs them. This will be very cheap if you can do it yourself or with a friend.
I'd also consider a new freewheel with shifting ramps and a new chain. You can probably do this for about $25 or less if you have a freewheel tool and chain tool, or if you have a friend with one. You will get smoother, cleaner shifts and a quieter drivetrain.
You may want to consider new brake pads (Kool Stop are very good ones) & cables and new shifter cables, if you haven't done that already. But if they're not rusty and working OK, maybe just oil them a bit.
Some people will tell you to replace the steel wheels with aluminum ones. It's true that this is a big upgrade in terms of lighter weight and also much better braking in the wet. On the other hand, it will be pretty expensive. I would hold off on that for now.
If you want new tires, Panaracer Pasela's are very good inexpensive tires that come in 27" sizes. Don't pay more than $20 each for them.
Hope that helps!
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1964 JRJ (Bob Jackson), 1973 Wes Mason, 1974 Raleigh Gran Sport, 1986 Schwinn High Sierra, 2000ish Colian (Colin Laing), 2011 Dick Chafe, 2013 Velo Orange Pass Hunter