Point one,
Firearms require ammo that must be reloaded, replaced and produced.
In the Zompocalypse, there will not be ammo factories etc. eventually You Will Run Out Of Ammo!
(2) Even suppressed firearms are noisy, this drawing attention of the zombies to your location.
(3) The amount of ammo you carry is Always limited.
What to do?
Swords, axes, spears do not require reloads.
Edged weapons are Quiet.
Edged weapons are much more easily replaced, repaired, produced. Especially spears.
Spears absolutely dominated the world of war until the advent of Massed use of firearms.
Spears give advantage of reach, which is also their primary weakness in close quarters combat.
Axes, there are valid reasons the Vikings preferred them. The disadvantage is range in CQB.
Swords, on the battle field were the back up, the weapon for CQB once the enemy got past the spears.
Personally,
My preferred load out is,
Spear/Lochaber Axe.
Long Sword
Tomahawk
Dagger
Working Knife.
Gauntlets
Maille
Greaves ( Roman style)
Helmet
Taken altogether the weight of that combination is less than a basic infantry rifle and ammo load out.
In fact, adding a Chainmail hauberk and helm, greaves, I am still carrying less weight than a modern infantry man, weapon, ammo, and body armor.
For me, 6’5”,
Maille shirt, 30 lbs
Helm, 3 lbs
Greaves 2 lbs
Long sword 3.5 lbs
Tomahawk 1.5 lbs
Lochaber Axe 3 lbs
Knives 1 lb
42 lbs total.
Compare to the modern full infantry combat load out.
Though, the maille, is not as bullet resistant as modern body armor.
Unless a Kevlar gambeson is worn underneath, or as an outer covering, overlapped kevlar plates like a Roman Lorica Segmentata
Conversely modern body armor is not designed to withstand medieval/renaissance weapons.
In the zombie apocalypse, I don't think armor will be an issue, unless it is zombie soldiers without firearms. Unless they are smart zombies and then, the ramifications are terrifying. ( 28 days later, 28 Weeks later scenario)
Either way,
If you wear armor, Zombie teeth and claws are much less hazardous.
Thus,
I present the following links
For information and education purposes.
Spear:
Long sword:
Axe
Dagger
These show a basic introduction to the weapons.
There are many available sources online. Hema is an excellent starting point.
Don't just survive the Zompocalypse, win it.