There are a lot of good used shotguns on the market these days too ...but Dave, Zippy, OneOunce and others laid it out for you ....
To start out with / you need an entry level gun that will let you play more than one game ...... I agree a pump gun isn't probably your best choice / but many of us started with pump guns when our budgets were a little lean ...
In general, ( I know you said no budget constraints but ..) that's kind of like saying you want a great 1911 handgun ....and someone comes back recommending a bunch of $ 3,000 guns / when what you meant was around $ 1,000 ....
Most of us that are Target shooters / look at levels of guns that will give us 10,000 shell performance a year / for a min of 10 yrs .....and that isn't going to be found in your "bargain guns" ....but not all "bargain guns" are poor choices either --- it depends. In general ....
pump guns will cost you around $500 - $700 ( like a Browning BPS Hunter model, 28" barrel, with screw in chokes ).
Many semi-autos ( Beretta 390 / 391 series ) around $ 1,000 ...
Over Unders - Browning / Beretta both make strong guns ...starting in the
$2,000 - $3,000 price range.... like the Browning Citori, XS Skeet model, adj comb, 30" barrels around $ 2,750 ......
There are lots of other options out there / with pluses and minuses ....but don't buy a gun until you spend a little time at your local gun club / try some guns / talk to some shooters / find out where they are buying guns - both new and used .....
Higher end competition level guns .... Perazzi, Blazer, Kolar, Krieghoff .....are very nice guns as well .... $ 8,000 - $ 25,000 / and if you really have "no budget" .....look at them /talk to some guys about them as well....
but I love my Browning Citori's (Citori XT Trap - for Trap / Citori XS Skeet - for skeet, sporting and bird hunting ) / my Benelli semi-auto Super Sports ...for skeet, sporting, bird hunting .... / even my old Browning BPS pump guns in a 12ga .....even though I don't shoot them much anymore ....lots of good memories there too ( and Zippy, Dave and OneOunce and others still have a little fondness in their hearts for a good pump gun once in a while ...)...