When I'm in veto mode, my first priority is always to eliminate the very few card interactions I consider legitimately broken: basically, this means I will veto to prevent the KC-Goons-Masq pin as well as the Possession/Ambassador or Masquerade trick. Most of the time, I actually prefer to keep Possession in there since I like defending against it. But my opponent(s) usually just take it out anyway.
Like many folks, I will often nix the really swingy attacks- but my definition of "really swingy attacks" is a lot more constrained than most and possibly only includes Swindler and Familiar. I'll sometimes take out Ambassador and Torturer, not because I'm bad at them but because they can be unfun. And probably about a quarter of the time I'll just go Random. But the three cards I love to veto, and take out whenever I get the chance, are: Duke, Baron, and Envoy. Duke is sometimes irrelevant (so a harmless veto) and sometimes screws up my heuristics bad (so a helpful veto); I don't quite know why but Baron inspires in me the same feelings of luck-frustration that many folks get with Treasure Map (which I usually just consider bad enough to ignore); and I flat-out hate Envoy with the burning passion of a thousand suns. It's a surprisingly bad piece of most engines, but it's great with dumb BM, but playing Envoy BM is even more soul-sucking than estate tennis or Torturer pins.
Unlike many other good players (it seems), I'm usually happy to keep powerful engines and combos on the board. Though sometimes I do inadvertently kill them with Random, and then oh well. In short, I will often veto to maximize fun, and while winning is fun it's far from the only thing that matters.
....
Yesterday I thought I had a shot at the top spot on isotropic. I tried for it, unfortunately Paralyzed reappeared and I have no way to surpass him (at least playing the way I'd like to.)
Meanwhile, I find that veto mode is actually good for boosting your rank if you are doing auto-match all the time. I don't think I've played significantly better, but the truth is I've never at such a high level before.
I've found my ranking has also shot up since they introduced veto mode, but I think that is much, much more a factor of playing "automatch to level +- 20". At one point I was second behind Paralyzed, and there's no way I deserved to have that spot. (I will say that the current top non-Paralyzed player, midnight_girl, is probably the best player I've ever faced- I've had several games against her and it feels like I'm usually getting massively outplayed even when I win.)