Preface: This is a generic guide not aimed at things like Magic Find, Gold Find, or special builds. This should be applicable to anyone getting into inferno and trying to progress.
Basic rules to follow when searching for any item (in order of importance):
Don't use round numbers when searching (prices for something with 199 int / str / dex are typically significantly less than ones listed at 200). This is because people usually only type in round numbers when searching and don't realize things are way cheaper under their limit.
First try sorting by newest listed. This is important for two reasons, one if an item is listed at a great prices chances are it will sell early. As such, your best bet for a good deal is looking at newly listed items. Similarly, if an item hasn't sold for awhile then there is probably a reason for it (stats suck, too expensive... etc).
Bidding is your friend. When looking for items, initially leave the buyout field blank because often times people just list items without buyouts and they are available for low bids. This is exceptionally useful when sorting by "least time left". Remember, bidding on items with buyouts can also be extremely effective.
Be willing to compromise. Maybe you wanted a weapon with a ton of STR / CRIT DAMAGE / VIT / SOCKET / LOH - but obviously everyone else does too. Figure out what stat is most important to you on that slot and then try and get minimal values of the other useful stats (or just omit them and try and get them elsewhere).
I am first going to go over some philosophy then get into each slot and explain what you should be looking for as you start out. This is completely generic information and isn't applicable to every build. However, if you use this mindset you should have no problems clearing a1 and a2 inferno without any issues.The most important thing to know when shopping for items is what stats appear where. I am going to break shopping for armor down into two groups:
The "middle" pieces (helm, chest, belt, legs, boots) are almost exclusively used for base stats, resists, and vitality. As such, you should make sure to focus on picking up as much as these three stats as you can on these pieces. I know shoulders aren't in the middle of the character sheet, but throw them in this list as well as they have no special properties.
The "outside" pieces (bracers, rings, amulet, gloves) are pieces that allow you to load up on all of the same stats as the middle with the added bonus of offensive stats like critical hit chance, critical hit damage, attack speed, and life on hit. Because these are the only places you can get these stats, you should make getting them a priority. Finally, as your income / gear improves you can start working on getting more stats on each of the outside pieces that you have been focusing on on the "middle" pieces.
Additional notes based on each gear slot:
Helmet: With the addition of Paragon levels, a socket has become mandatory... end of story. You can actually pick up crit here as well but it is expensive early on. I would focus primarily on base stat + socket + vit / all res initially.
Chest/Pants: I search for these in an almost identical fashion. The only main difference is that the chest armor can have one more socket and also have life% as a stat. When starting out look for Base + Vit + AR + Sockets. That being said, I always try and look at the total amount of vit + base stat before sockets. For example, 130 int 100 vit + two sockets isn't as good to me as 80 int 200 vit + two sockets even though it does less damage. You are looking at, effectively, 230 base "points" vs 280 "points" that are useful to your character. The additional vit here could let you omit it from an "outside" piece.
Boots/Belt/Shoulder: These three are very similar to Chest / Pants except they can't have sockets. Belt and Shoulder can have +life% which is useful and I pretty much consider Run Speed bonus a must on my boots. Overall these are three of the easiest slots to search for.
Rings: Here is where it gets tricky. It is often really hard to determine if Attack Speed + Crit is better than Attack Speed + Crit damage or maybe even Crit Chance + Crit damage. All in all I would just suggest focusing on getting as offensive as you can with these stats and use the calculator (listed below in resources section) to compare rings from the AH. Also remember you can pickup LOH here which might not up your damage, but can greatly help with your survivability. Finally, do not ignore the +max or +to min damage affixes. They are extremely valuable as they increase your base damage (which in effect increases the value of all of your gear).
Amulet: Very similar to rings with the exception that these slot can have HUGE + base stats. Try and pick up as many offensive stats as you can while also looking for some vitality and all res. This will not be a cheap slot.
Bracer: In my opinion, all res and crit here are a must. Bracers are getting increasingly cheaper and finding ones with Base stat + vit + AR + Crit is easy enough even under 100k.
Gloves: This slot can be a damage boosting power house. It has the ability to get the "trifecta" (crit chance / damage / attack speed). Typically when starting out, I tend to ignore defensive stats on this slot in order to try and pick up damage stats that I can't find on other pieces of gear.
When starting out, weapon damage is king. When starting out the single best thing you can do to up your efficiency is to look for higher damage. I know you're used to playing a caster in WOW where stats were all that matters, but weapon damage is by far the most important and here is a quick explanation as to why:
Every point of base stat you get (str / dex / int depending on class) increases your damage by 1% of your base WEAPON damage. So, unlike many games, your base stat doesn't affect damage at a flat rate based on your character or build. Instead it is based purely off of the base damage your weapon does. So getting a higher damage weapon effectively increases the value of every other piece of gear you have with a base stat on it.
*note there are specific builds (ex. WW Tornado Barb off hand item) where this does not apply.... this is a generalization
When hitting higher gear levels, weapon damage becomes less important. It is necessary to understand "less important" does not mean unimportant. Weapon damage is still critical to your build. But when you can start affording weapons with sockets or very high amounts of critical hit damage (to go with that crit you have been getting on gloves / rings / etc), lower dps items can out perform your current item.
Focus on weapon unique stats first. Yes you can get stats like LOH and crit damage on rings and amulets, but the weapon is often the easiest place to load up on it for a cheaper price than the other slots. It will be way cheaper to find a way to get an extra 100 base stat on your other gear than it will be to get 700+ LOH or 80% crit damage on other pieces of gear. As such, these should be the stats you look for first when shopping for weapons. Start off by searching only for these stats, and if you can afford addint base stats or other "like to have's" then by all means go for it.
Weapons are a great place to pick up vitality. A lot of times vit is completely undervalued on weapons because people think of them purely as offensive pieces. If you want to drop base stat on a weapon, try and make sure you can get some vitality on it. Adding even 170 vit on a weapon is like adding an entire other piece of gear when at low gear levels.
Mojo / Source: The most important stat on these (unless looking at a special build) is their damage range. Ideally you want the highest average damage possible (mix + max / 2 for those of you not math inclined). After that you want to focus on off hand specific stats such as Crit / AP on Crit / Mana Regen / Max Mana...etc. Finally, look at base stats + vit.
Shield: The ultimate stat stick. The most important stat on it is it's block rate, but other than that just get whatever you want. They can have huge bonuses to base stats as well as crit and AR. Basically just fill in what you're missing elsewhere here
TLDR: As much base stat / vit / ar on shoulder / chest / belt / helm (socket) / boots (move speed) as you can get. Offensive stats on gloves. Bracers AR + crit is a must. Rings + Amulets load up on offensive stats. Focus on high weapon damage early then move to sexier stats like LOH + Crit damage later.