Skillwise: I recommend you max only "Ranged Mastery", "Critical hit", "Explosive shot", "Adventurer" (this is for more xp = more levels = more skills). If you eventually go further than this you can max the last skill "Arrow hail" of "block and parry". Personally I would not use block and parry, unless you are going for an exotic melee variant of the vanquisher. I find it much more usefull to let your pet do the tanking and shoot them from afar. These are all marksman skills. I have never tried either rogue or arbiter. Although the electric bomb of the arbiter skillset can be usefull in the beginning of the game when you dont have explosive shot. I would only put 3 or 4 skillpoints in it though, as explosive shot will become your main skill (it is extremely overpowered, I can't believe they didn't notice this during beta testing).
Itemwise: DPS, DPS, DPS. Whatever you think works best, I prefer a fast rifle instead of two slower handguns, although the extra slots and enchantements the handguns give are indeed very usefull if you are trying to get the most DPS out of your Vanquisher. I also found that sometimes a slow but very powerfull rifle works better in certain occasions, as you will (if you have enough dexterity and crit) be able to one-shot most foes. This will save you potions since the monsters won't reach you. However once your explosive shot has arrived you won't be auto-attacking anymore (it costs almost no mana, is very fast, crits for like 4000 AND has an AOE of 6.5 metres, its insane). So after that i would go for enchantments that make you attack faster. If you don't like spamming explosive shot (it can get very boring at times) you can try to socket your weapon to one elemental damage only. For instance you pick ice = try to enchant/socket your other items so you get extra ice damage.
The pet: I gave it spells that reflect damage and trinkets that gave extra health, since your pet will take the most damage it needs high health and the reflect is usefull for that extra damage to monsters. The second spell I would choose an offensive spell like fireball or something. Or you could let it summon zombies or archers, always fun to just let your pet roll in with its minion army and see them take down some creeps :)
Thats it for this very simple, standard build, I assure you that you won't be having much trouble killing stuff while staying alive. Just don't forget to upgrade your armor often, you don't want to be one-shotted now do you :)