Accumulated from various threads and contributions that demonstrates
anxiety, not research:

As far I can tell from advice on HF, the thin foil doesn't shield as well at
HF as a thicker braid with good physical coverage.

It sounds like you should stop listening to advice on HF.

I found an RG6 at low cost with copper braid and Al foil (more likely
metalised plastic film)

....and hence mostly likely NOT RG6. RG-anything is barely more than a
public domain trademark. This been hammered to death already so any
appeal to nomenclature should be confined solely to the physical
attributes of wire radius and shield inner radius; and NOT the number
of shields, NOT the coverage of the shield, NOT the property of the
wire being stranded or solid, NOT the property of the shield being al
vs. cu. Everyone of those prohibited-for-discussion characteristics
varies between manufacturers sharing the same nomenclature.

The standard for cable tv and satellite instalations is RG6 "quad shield",
which has a less dense braid, but a (almost) 100% aluminum foil shield.

Foil shield is a gap filler, NOT a conductor in the conventional sense
of long runs. There are no coaxial cables that have only a foil
shield (a plastic carrier of a metal deposition) that are useful for
any antenna work. Hence, the property of foil alone does not bring
any useful quality to the discussion.

As far I can tell from advice on HF, the thin foil doesn't shield as well at
HF as a thicker braid with good physical coverage.

Abysmal sources of information should not be returned to. "Thin foil"
is a gap filler, not a shield.

Besides, most advice out there implies I
have to buy it and try it to be sure, which is stupid because it's cheaper
and faster to get a better cable! RG6 is specified for UHF, I want HF.

RG6 does not have a specification for frequency ranges outside of
loss. In that regard, RG6 is eminently preferable for use at HF over
UHF for that one consideration alone. There are cables of other
physical geometries (about the only thing that counts in this
discussion) that exceed the performance of generic RG6.

http://www.abccables.com/info-rg59-vs-rg6.html is one of the more descriptive
texts I read.

Interesting? Quite banal, in fact, when one stumbles over such
statements as:
"A basic rule of thumb is to use RG6 for any
Rapid Frequencies, and use RG59 for
video frequencies."
Now there's an authoritative standard you can take to the bank (if it
is AIG). Perhaps they meant "Vapid Frequencies."

I must admit I do not understand the theory that foil is worse than
braid at lower frequencies, foil gives 100% coverage and is usually in
addition to braid. Even if it the thickness of the foil that is in
question, I don't see how, according to the article that you linked to,
it " don't(sic) have the proper type of shielding ".

Foil, as pointed out, is in addition to standard shielding. Foil
bridges the gaps between the wires composing the weave of the shield.
Those bridges are highly conductive over the very short distance
between adjacent wires, but as a conductor, foil is miserable as a
sole conductor. That is why foil shields that are the sole shield
have what is called a "drain wire" running the length of the cable. It
is quite obvious that such cables have enormous loss per foot in
transverse mode, but these shielded cables do not operate in that
fashion as they are almost exclusively supporting paired conductors
(twisted pairs that are the signal carriers). Hence, these
applications of foil/drain-wire are limited to low signal use where
the shield will encounter small fields. Even then, they can be
marginal.

That article does seem to have a few vague contradictions,
but I think the point about a thin foil that is adequate for UHF screening
being inadequate for HF is interesting, and I've seen that point claimed
before.

In coaxial application, the performance of the foil is limited to its
thickness, which in turn can be penetrated by low frequencies. We
know this as an example of penetration depth. The surrounding wire is
probably 10 to 100 to 1000 times thicker in that regard. The wire
will always satisfy most typical applications (VLF and up) and where
it would not is found in "coverage." Such issues are very rare and
are not elevated to important simply because you are straining to
catch a weak signal.

Even with this shortfall, one has to consider. On the one hand you
have a 90% coverage cable that gets signal into it. You add a poor
conductor like a metal deposition plastic covering (aka foil) and it
reduces that specific leakage by 3dB. To buy that 3dB in additional
conventional wire coverage may boost the product cost 10% whereas
adding a foil boosts cost only 1%. By reputation around the pickle
barrel, the foil is still a poor solution, but in a particular
application it bought you 3dB that you might have walked away from.

This, of course, is a fantasy scenario to illustrate how a technical
decision is weighed against cost and need. Unfortunately this fantasy
scenario exceeds the technical discussion found in:

I like that BT2002 with the double copper braid, but I'm not yet sure
if the difference justifies the cost

Sole cost based decisions for technical problems rarely prove useful.
You are going to have to decide whether you can accept the performance
you thought you paid for, or pay for the performance you need. As you
have not actually specified any quantitative characteristic, you are
facing either disappointment or illusion.

73's
Richard Clark, KB7QHC