Welcome .....
Browning - Winchester are both owned by FN these days. The Winchester SX 3's are very similar / to the Browning silver series ( activ valve systems, etc).
I like the inertia systems - they shoot cleanly / but unless you buy the versions with the "comfort tech" recoil supression system in them ( they have chevrons that compress in the synthetic stocks ) then it'll give you about 25% more recoil than a typical gas operated semi-auto shotgun.
As long as you stay with Browning, Winchester, Beretta and Benelli shotguns - you won't find a bad gun in the mix. They're different - they "Fit" differently --- have different stock dimensions - different drop at comb, drop at heel, lenght of pull, etc ...so you have to decide what best suits you.
For a good all around gun - some clays, some hunting, etc - personally I like a semi-auto shotgun with a 30" barrel. The longer barrel gives me a longer sight plane - and smooths out my swing on follow thru / especially on the lighter guns - like some of the Benelli's. If you think 30" is too long / or it doesn't feel right - then go with the 28" barrel. In most issues a gun chambered in 3" is plenty / gives you plenty of options for shells. Some guns are chambered in 3 1/2" - and marketed to the waterfowlers - so you can shoot super magnums ....but I've never seen the need for a 3 1/2" gun.
For a first shotgun - I would recommend a gun that comes with some adjustability - like shims between the receiver and the stock - so you can adjust the angle of the comb a little. Beretta, Benelli - and some of the Brownings have shims / but a lot of models don't ... If you're looking at any used guns - make sure they have changeable screw in chokes. Some guns made prior to 1980 or so / will not have changeable chokes.
and shoot as many guns as you can before you decide ... hang out at a gun club / ask about what guys are shooting - and why ...and would they buy it again. You'll probably see some trends ... on the "budget end" and on the "higher end" ...and it'll help ...