Robert, I had to check your OP (original post) again to make sure I didn't get the zeros wrong — a five and then 3 zeros — not 2 zeros....
Excellent! With your budget the sky seems to be the limit!

That's great!
THE GUN
GUN POWER PLANT If you want QUIET — PCP is the only way to go. Especially if adding a silencer. Springers like your D34 don't benefit very much from a silencer as the main noise comes from the action.
GUN BRAND You probably want a high quality brand. Some were already mentioned above.
GUN STYLE ▪Do you like a traditional stock — walnut wood — stipling and similar features?
▪Or do you like functional and tough — synthetic stock?
And would you like a bullpup? For most that's an either hate-or-love choice....
GUN CALIBER ▪A .177 is quite sufficient to kill starlings.
▪If you happen to have significant wind you might benefit from going with .22cal, as the .22 pellets
generally have a higher BC and are thus not as sensitive to wind drift. (Wind drift for airgun pellets is much, much more than for a powder burner, especially if you shoot beyond 30y.).
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THE SCOPE
SPRINGER-APPROVED SCOPE: NOT NECESSARY If you have a PCP it
won't be necessary to buy a spring-airgun-approved scope, so you got all your choices open (the D34 is known to be a scope eater...).
FIXED OR VARIABLE MAGNIFICATION You know the benefits of either, I suppose.
Since airgun targets can pop up
really close, and then again you might want to get that starling
far up in the tree at 50y, it is a huge advantage to have a variable magnification.
If I understand correctly, scope quality has improved in general over the last decade or so — that even $200 and $300 made-in-China scopes can deliver pretty good quality —
even if they have variable magnification!
MAGNIFICATION RANGE ▪TOP END: If you choose a variable magnification, the top end of your magnification range depends on your maximum shooting range, and on the quality of your eyes.
In my case, the first seems to be ever increasing, and the latter decreasing — somehow these two things don't line up for me....
Airgun quarry are tiny and so in general a larger magnification than for powder burners is desirable.
▪BOTTOM END: The bottom end of your magnification range depends on how close you want to take quick rushed shots — and thus
need a large field of view (FoV) — in order to acquire your target rapidly.
Airgun quarry can frequently pop up as close a 10 yards, much closer than the typical powder burner shot. So, a wide FoV is desirable.
FFP or SFP — and RETICLE AND TURRETS First focal plane (FFP) or second focal plane (SFP)? You probably know the difference, however, airgun pellets drop a lot more than powder burner bullets — which means
you'll have to adjust your point of aim (POA) much more often with airguns for a range different than the one you zeroed your gun for.
▪If you chose to use your reticle to make POA adjustments — then you'll need a reticle with
evenly spaced hash lines (not a BDC or a plain reticle) = I call it a holdoff reticle.
In an
FFP scope the distances between the reticle hash lines do not change
in relation to your target — so no matter what magnification you choose the holdoff/ holdover that you have on your dope card or memorized is always the same. In an SFP scope these change for every magnification.
▪If you chose to use your turrets, get a higher priced scope where the turrets track true (many seem to have pretty good experiences with scopes starting around $3/400).
▪If you like to use both for different shooting scenarios, get both features....
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I'll attach three Scope Specs Tables for three different magnification ranges below, comparing the specs of around 200 scopes that are suitable for airgunning:
▪10 yard minimum parallax — for those close shots (the list only lists
side parallax scopes, not OA at they are less convenient to adjust)
▪Holdoff reticle — for POA adjustments
▪Exposed turrets — for quick adjustments of POA
▪The list focuses on $500 and under
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THE SILENCER
There are plenty of airgun silencers out there.
Some a plain pipes.
Some have indentations, nooks, and moldings — looks nice.
➔➔

I'll attach a Silencer Specs Table below comparing 50 silencers.
Robert, I wish you HAPPY SHOPPING!! 
Matthias
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ATTACHMENTS BELOW
View attachment SCOPE SPECS TABLE. For 4-14x 3-18x, 4-16x Magnification. 074. 2020-09. TABLE.1602379028.pdf View attachment SCOPE SPECS TABLE. For Short Scopes -and- 3-12x. 045. 2020-08. TABLE.1602379061.pdf View attachment SCOPE SPECS TABLE. For 6-20x 6-24x, 5-20x, 5-30x Magnification. 116. 2020-09. TABLE.1602379082.pdf View attachment SILENCER SPECS TABLE. 17. 2020-10. TABLE.1602379104.pdf View attachment SILENCER SPECS TABLE. 17. 2020-10. PHOTOS.1602379125.pdf