I have an 1982 or 83 vintage M1894 and it does not have the side safety.
I am of the opinion that the push button safety is a safer mechanism.
But since your does not have the push button, you need to be aware of a condition called "false half cock". You can perform a web search and see pictures, at least of a M1911 mechanism, describing false half cock.
It is possible to balance the hammer on the sear, not in the half cock notch, but on the notch edge. This is an unstable condition. With a little force anywhere in the system, on the trigger or hammer, the hammer will slip past the sear and you can have a discharge.
You also need to be careful when letting the hammer down and not lose control of it. I wish I knew a better way to do it, because you have to pull the trigger to let the hammer down from full cock, and if you lose control, it will go forward and ignite the cartridge.
I used to dry fire my M1894 but the firing pin broke. You can dry fire with mechanism with the push button, but I don't recommend it for the older models.
It is unsafe to carry a round in the chamber and hammer down.
I hope you enjoy your Marlin, it is a fine rifle.