Nobody has asked the OP whether the amplifier has a Power transformer as part of the power supply .
If it doesn't have one,it either uses a switchmode power supply,or is that most deadly of things-A Transformerless,or "AC/DC " supply..
If it is the latter,my advice is to cease & desist now!!!
In such power supplies,the chassis is connected to one side of the incoming Mains---the Neutral side,if the plug or power socket are wired correctly.
The "Active" or "live" side is then rectified directly.
All OK,if a bit horrible,if it is the Neutral on the chassis---but with Active on the chassis,touch it & a real Earth,& in the words of an old Japanese Safety note:-
"It is utterly sufficient to send you directly to the heavens"
Such supplies were widely used in some countries,with heavy insulation to protect the user,but "homebrew" versions usually don't have such protection.
There is no justification for such supplies in an amplifier built in 2015 --------If you don't like linear transformer type supplies,use an SMPS,they are reasonably safe,plus are probably a factory made unit,in any case.
This brings us to an "old style" transformer type supply.
The series lamp idea is to protect against short circuits,or things which are not exactly shorts,but draw excessive Mains current.
They are mainly used when restoring a very old piece of equipment which may have problems.
The Primary side of a transformer tyoe supply is quite simple,& may be checked out without power applied,(AND with the cord unplugged from the Mains socket) using the DMM's Ohms range.
With this,you can check whether your ON/OFF switch actually does what it is supposed to do,& doesn't short Live & Neutral together-------don't laugh,I did that as a beginner!!
Once you get past that hurdle,you should,with the switch "ON" be able to see the resistance of the transformer primary across Neutral & Live.
Check for shorts to chassis,& hence to Mains Earth,on both sides of the power cord.
With tube rectifiers,the next step was to remove the tube,then fire the amp up ( having taken the DMM probes off the circuit.off,& switching that instrument back to its highest AC range.)
This will test all the primary & secondary high voltage ac wiring,plus the filament wiring.
This step is a bit messy with solid state rectifiers,& I would suggest be dispensed with.
Instead,check the rectified HT circuitry for shorts,Incorrectly polarised electrolytics,etc.
Visually check all the wiring twice,& if all looks ok,unplug the tubes & fire it up.
No smoke?-switch the DMM to dc & look for correct HT voltages out of the power supply.
Go to ac on the DMM & check for the presence of filament voltages on the appropriate pins.
Finally,turn it off,restore all the tubes & turn it back on-------if it is an Audio amplier which feeds a Loudspeaker,make sure one is attached,of the right impedance & appropriate power rating.
Safety---easy----this thing uses high voltage DC anode supplies,so you can't just poke around inside like you might with something having a 5v or 12v supply.
( I was going to say "a solid state circuit" but many such circuits use voltages approaching those used with vacuum tubes,so it is no longer a valid comparison).
There are also places you can get bitten by 200-300v ac from the transformer secondary,& the Daddy of them all,is of course,the Mains!.
There is no need to be terrified,though,you do hundreds of things every day,which are more hazardous.
As a former Australian Prime Minister said in a different connection:-
"We should be alert,but not alarmed".