Assuming that you obtain one in good condition, the BRNO is a solid contender. For your stated purposes, I don't see why fixed chokes won't fill the bill (I didn't see any references to skeet). For trap, you'll do best with a configuration such as F/M. I often hunt the uplands with guns choked F/M, but the area that I hunt includes large open areas. So, we're presented with both close shots in tight bush as well as long shots, as the birds often break cover and head across open areas. Tight bush conditions, such as our Eastern colleagues describe, may lend themselves better to more open chokes and the choice of skeet to employ those more open chokes at the gun range.
I'm practically a broken record when it comes to shell selection but, once again, I'd recommend using Gamebore Pure Gold or equivalent shells that have felt wads rather than plastic shot cups. In addition to not leaving plastic shot cups everywhere, these shells will allow the fixed chokes to do their job properly, instead of keeping your patterns even tighter than the chokes demand (assuming we're not talking about "spreader" cups or the like).
It has always been my personal philosophy to own numerous guns, each with advantages and disadvantages for given purposes. This approach has cost me birds due to momentary confusion in the heat of a bird busting cover. Trust me, you don't want to be switching guns even occasionally if maximum bag is your only goal. I don't care if on occasion I forget that the gun in my hands has an auto-safety. I consider it part of the bird's sporting chance to escape that I'm never fully instinctual with my gun due to using all sorts of different makes and designs.
This doesn't for a second mean that one can't be successful at many sports using a single, multi-purpose gun. But it does mean that you want to be aware of your personal philosophy in this regard and that your choices should reflect the specific, or the more general, nature of your intended usage.
Without knowing you or knowing where you live, I suspect that a Tradex U/O is an excellent choice for a gun at this point. I also anticipate that you'll get your money out of it if/when you outgrow it and your needs evolve.