Pretty much what tggzzz said.
Understand probes and probing, compensation and the effect of ground leads. It's amazing how many engineers and techs don't understand them fully after years of use.
I always look inside whether or not I should. If it's filthy, a safe and easy way to effectively clean it is to hold a vacuum hose near an area and gently agitate the dust and dirt with a natural bristle brush. Avoid high velocity air as you will develop ESD and may cause damage.
Some years ago, I bought a 2213A demo from Tek and loved it. One day it would not power up and I discovered that one of the power rails was shorted to ground. The challenge is that there were maybe 50 or so capacitors on that rail. By careful measurement I was able to track it down to 1 bad cap and all was good again. Never had another problem.
For general use, you may want to take a look at dc accuracy (which will also cover your low frequency uses). If you can find schematics you can determine if there are any gain or offset adjustments. If not, just keep a mental reminder of errors. For critical amplitude measurements, click the Y knob into variable position (been a long time, I think it can do this ??) and adjust the trace amplitude against a known source. If your calibrator is accurate, use that. If not, build yourself another square wave oscillator with any CMOS, even a CMOS 555, and an adjustable supply voltage for it. An adjustable LDO is good for that.
On a 60MHz analog scope, it's difficult to impossible to look at signals with low repetition rates. If you're trying to observe the characteristics (amplitude, shapw, etc.) of a low rep rate signal, if you can force your signal to repeat more often, you will be able to examine it.
First scope is up there between first car and first child in excitement level it generates. Our favorite pizza shop is a mile down the road. The owner ran an electronics company in his former life. One week he was cleaning his basement and asked if I wanted some junk. While I chowed down on lunch, he disappeared and actually went home to get the stuff. He returned with a very nice GenRad Digibridge, digital readout and accurate but definitely no frills. The second items was an old Dumont / Fairchild 401 scope. I almost wet my pants. This was my first scope in my late teens, FIFTY years ago ! This ones needs lots of tube help so now is sitting on my shelf instead of his.
Sorry for the long-winded story. Enjoy the scope !