i suppose what i really am asking though is what is the best way of
getting rid of the existing weeds / stalks / flowers that are covering
my garden.

That's what the cardboard/newspaper suggested by someone else was
for. Deprive them of light.

But there are different ways to go about this. Digging or pulling can
work. Some sources will suggest herbicide (although if you do want to
go this route be careful about how long your chosen herbicide lasts in
the soil and other such considerations).

Given that you have a relatively small area, I wouldn't be afraid of
pulling things up by hand.

Personally, I always tend towards the "identify the inherited plant
first, then I know whether to keep it or not" approach. But that
could take you a while with 3+ years of untended growth (a few of the
plants you'd identify pretty quickly, but there are lots of plants in
this world and it takes a while to learn all the ones in your yard).
So I wouldn't blame you for sticking to the "get rid of it all and
start afresh" plan.