The most useful skills? In Cunning: Fast Hands, Ambush, and Rising Shot. Fearless is more situational and the bonuses it gives are small, but it's still worth getting. Two Fang is okay--the second shot does deplete ammo and adds to recoil, but those are its only downsides. The other skills--Unforeseen, Counterstrike, and Innervate--don't have much use on a gunner.
Death Blossom/Death Mark stacking is useful no matter what your build is. The only reason not to get it is if you're going for Critical Ascension.
The Sniping tree is kinda hit or miss. One Shot One Kill and Bore are good for almost any gun build, but the rest of the skills are...less so. Most people get Headshot and Killer simply because Optics and Precision are highly situational at best. Past Bore, the rest of the tree is really up to personal preference. Velocity is good for the bullet speed, but the critical hit damage bonus is off (it adds much less than it says it does) and the gun damage bonus is really small.
For class mods--look for Disturbed Stalker if you like pistols, One Shot Sniper for sniper rifles (the additional critical hit damage isn't that useful, but the bonus to base sniper rifle damage is) or if you want to boost OSOK past 5. Professional mods increase reload speed, and combined with Fast Hands and Killer you can get your reload speed fast enough to reload certain guns faster than they can shoot, so you can make use of OSOK more. Survivor mods can add to Rising Shot and Ambush, but they only give health bonuses.
Pistols and shotguns with low capacity magazines work well with Zer0's skill set.
What everyone needs to do is calm down, take a deep breath, and prepare their bodies for the Thunderdome. GT: janejana