Let's go through piece by piece, starting at the top.
Helm - Zuni's Vision is cheap, you shouldn't have a problem getting one for a few hundred k. You won't be able to afford crit or allres, so try and get high life %, high int, and either a str or dex roll. Str is extra armor, and dex up to about 500 will give you significant dodge (up to about 20%). A double int roll is nice if you can pay a little extra.
Shoulders - hands down, crafted archon shoulders of vitality. Craft until you get an int + allres roll. Shouldn't take too many tries. Shoulders are defense, make sure you have allres. Armor, life%, and str all are good too, you can settle for little or even no int while you work on other pieces.
Amulet - craft either amulet of vitality or intelligence. vitality can work for any other hardcore classes. Either way, you're looking for lots of damage stats here. The most important stat is probably crit chance. Crit damage, high int + vit, average damage, life%, allres are all good rolls. I would settle for anything with crit chance and int/vit (depending on the ammy type) to begin with. Lots of potential to upgrade along the way.
Chest - You'll want a zuni's marrow. The cheapest ones are roughly 40m right now, so until you get some gold rolling use rares. I've heard some good things about crafted chests, but they can be expensive to make. Simple piece, you just want int, vit, allres (50+) and possibly sockets.
Gloves - craft int archon gloves. You want to roll crit chance at a minimum. After that, look for crit damage, allres, and vit.
Bracers - craft int or vit bracers. You want allres and either int/vit rolls to start. After, come back from int/vit/allres/crit chance.
Belt - rare will do. Look for int, vit, allres, and any other bonus stats (str, armor). Hint: instead of vit, look up life%. should save you some money.
Rings - you want a Zuni Pox. current price, about 30m. Until then, rares are find. Rings are extremely flexible, so look for them last to fill in stats your other gear is missing out on. Also, don't look for trifecta or common popular cominations (ie. int/vit/avg dmg). If you look for more uncommon combinations, they can be cheaper (i.e. allres/crit dmg/avg dmg). Try an get at least one crit chance, one crit damage, one avg dmg, and at least one high allres roll between the two rings.
Pants - high vit, int, allres. str or armor is a plus. you won't be able to afford sockets at this point.
Boots - Zuni Trail are about 20m now, so probably get them after the mask. Until then, you want anything with ms/allres/int/vit. pretty basic. Give up int or vit and try to make it up on another piece, this usually saves gold.
Offhand - Thing of the Deeps and Uhkaps are what you're looking for. Average damage is the most important stat. These two have natural crit and int rolls, so look for bonus things like mana regen or high dmg to elites. Focus on avg dmg, you'll eventually want 200+
Main Hand - Manajuma's Carving Knife. Get the highest dps in your price range, but ones in the 800's are less than a million gold. The crit dmg and int make up for the lower dps. If you find a ceremonial knife or rare one hander with 1000+ dps, go with that. Just keep looking at Carving Knives, and see what's better for your dps.