I was thinking, if I was to look for the most redshifted stars,
and did assume a big bang, and the redshift caused only by Doppler,
then the most redshifted stars would be the furthest away, but just
as old as our sun?
This is why I think that:

Origin of BB:
O

After some years, A and B are stars speeding away from the BB origin:
A O B


After even more years:
A O B



Now suppose we are on star B, then for us star A will move faster away
then any star in position O, so star A will be more redshifted.

So when we look at the most redshifted stars, we merely look at the ones
that are speeding away at the highest speeds, and that are those on
the 'opposite' (sorry 2D picture) of the BB origin.

But they often say: 'this (the most redshifted) is the oldest......'

So where am I wrong?