1: Where you gamble has not effect on the result. I think the difficulty level matters though.
2: Character level does matter a whole lot. I would go as long as to say it is the defining factor in your gambling. This should not keep you from gambling at lower levels, but if you want something important always use your highest level characters.
3: Rings, amulets and circlets are arguably the most popular as they can get some pretty sick mods, but there are other things to gamble too.
Gloves can come with some pretty hefty resistances and neat stuff such as Increased Attack Speed, amazon or assassin skills or Magic Find.
Gambling weapons is another good alternative. Now that the top damage mods can appear on rares you can potentially get some pretty nasty things. A good blue Cruel <something> of Quickness or Cruel <something> of Evisceration is not a bad thing either.
Be sure to keep any one-handed weapons of Sounding. Barbarians love to have them on switch for Battle Orders.
Assassin claws are also nice as they can come with some helpful skill mods or just be helpful at lower levels.
The only thing not to gamble for in my opinion is armours. There are simply too many good unique or set armours to make it feasible and they are rather expensive to gamble too.