Check this site for a bit of how your carb is set up.
pics # 7, 8, 9 show your type of carb.
#10 shows the diaphragm (it's on the backside from the photo you posted)
The fuel mix screw is above the tan/yellow looking tube in pic #9
about 1 and 1/2 turns out from gently closed.
if needs more than about 1/4 turn either direction to run, then the carb needs attention.
that's generally just the new diaphragm (pay close attention to how things come apart)
and a good cleaning. typical issues with stale gas, varnishing, plugged passages etc.
water in those steel tanks give you rust and on older tanks can make it
difficult to keep your motor running.
Those two tubes hanging from bottom of carb (where it is screwed to tank)
have screens and may need cleaning, not tearing out,
as an old mower wrench I often saw this done, it doesn't fix the problem.
Also note that you can flood these engines with that choke if you miss the first pop.
when you get that pop, push the choke about half way back in (open) and crank again then ease the choke open as the engine warms.
after a bit of practice, you'll probably get that ...
pull the choke,
pull the rope and as the engine coughs over,
pushing the choke as it revs up till it's warmed up.
usually in one or two pulls when everything is *dead on tuned*
and no worn parts.
The starter clutch will need a couple of drops oil in it.
just three 1/4 bolts
people will listen to that squealing until it grabs on the top of the crankshaft and spins
which then rips the recoil apart.
if it ever squeals, take it apart and clean the crankshaft and inside
the starter clutch hole.
at the point of squealing it's too late for just oiling and you *really*
need to do the disassembley and cleanup.
the carb pics (info covers more than one type carb and a bit jumbled )
Disassembly, Cleaning and Repair of Briggs and Stratton Tank-mounted Pulsa-jet Adjustable Carburetor - Horizontal Crankshaft Engine
and a pretty decent thread on the starter clutch
balls in the basket cleaning the starter clutch - OldMiniBikes.com Forum
If you don't find what you need in the links, give a shout
and I'll see if I can shoot some useable pics.