Welcome to my Massive Skill breakdown post!
This is just my general opinion on the skills. Some are utter trash obviously, and some are gold, and others are of questionable use.
vBAddict has way more detailed info on a per-tank basis and should be the preferred source. http://www.vbaddict.net/tankstatistics/overall and then click the tank you want and review the crew skills for that tank.
Many thanks to @8_Hussars for reading this and correcting a few things and Links!!
This entire list is Tank-agnostic, which mean's that it's not built for anything specifically. It's just a general review of the crew Skills. The higher up the skill is, the more priority it should have/better it is.
General Crew skills:
All of these require it to be on every crewman to be at 100% and it's averaged out. For a 5 man crew, with 2 people with camo and 3 without it looks like this:
(100+100+0+0+0)/5 = 40% effective camo. (or repairs or FF)
BIA also boosts the effectiveness of all 3 of these skills. Camo and repairs are generally your first skill out of the box, but which one you run greatly depends on the tank and your playstyle. This one is odd because it's a Perk AND requires ALL crewmen to have it at 100% before it's functional at all. Now compatible with the Female Sisterhood of Steel perk! yay! Girl commanders and Gunners for all! (also with the Sabaton special crew)
BIA: always useful, but it's MORE effective if it gets trained as a 2nd or 3rd skill due to the way it works. (+5% to general crew skills (repairs FF camo) and to major qualifications, but not to, say Recon or Snapshot) Requires ALL crew members to have it. It's a perk so its 100% effective only (also a good reason to train it 2nd or 3rd)
Repairs: (Skill) are pretty much a 'must' with meds and heavies, esp tier 8+. Fixes everything faster. tracks, turret rings, gun etc.
Camo: (Skill) is a good idea for scouts and most mediums. It's a waste on most heavies, but critical and useful on others! (IE: AMX 50B) Do your research on tanks.gg!
Firefighting: (Skill) is actually useful if your tank gets set on fire a lot. see This spreadsheet and Thread on effectiveness. (fire dmg -10%, no extra chance to save modules). Run an AFE if it's that much of an issue and save the skill slot for something else.
Commander: 6th: #1 best skill ever. running a tank without it is voluntarily just trying to give away health to baddies. Recon: +2% VR and a good skill. If you can put Sit Aware(3% VR) on your Cdr do that first. Seeing them before they see you = good. JOAT: Useful skill on tanks that get crew members knocked out a lot. Probably a good 4th skill in general. Doesn't stack with anything, but it's fairly useful for non-Large Med Kit equip setups if you prefer to run food instead. (or your driver likes to die a lot like on Chinese Heavies) Eagle Eye: There's some use for this skill in personal missions. Esp in high ROF/Auto tanks and super caliber tanks due to the way that module damage is computed. Functions the same way that Designated target does. (your crew has to spot the tank and then your gun has to be pointed at the tank for a few sec to see if anything is damaged. DOES work with arty.) Mentor: Treat it like a perk and retrain it to 100% and keep it on. Really only useful for 6+ men crews. and then you waste the skill slot. Just let it go....
Gunner: Snap Shot: Pretty useful for all tanks, even casemates and arty. Reduces bloom by 7.5% on turret rotation/Gun movement (3.5 effective). Works great with Vstab! Does stack with Driver's Smooth Ride skill Deadeye: also fairly useful! extra chance to break stuff is always a good thing! AWESOME on auto loaders and high caliber hitters. High ROF tanks and super caliber tanks get some nice benefit from it due to the way that module damage is computed. (it's basically an overmatch rule, similar to the 2x mechanics. some supercalibers can get into 3x turf vs medium/lights tanks.) This is one of my favorite practical skills. The extra dmg to De-Track (all that tasty track dmg bonus) and also to maybe wreck someone's crew/modules is entertaining Designated target: Great for scouts (just autolock and run), Some meds. 400+ base VR is a good candidate for this skill. Works the same way that Eagle Eye works. Heavies, unless you need it for a personal mission skip it. Armorer: train Repairs before thinking about this skill, then train this. Repairs works for all red modules and tracks, Armorer only works on improving the accuracy of a busted yellow gun. shooting > not shooting.
Driver: Off Road Driving: Best skill a driver can have, improved movement on non-paved surfaces and you can outturn someone with clutch braking. Good for fast tanks. Clutch braking: 2nd best skill! tiny bit faster deg/sec PIVOT turning (A/D only not W/S) than ORD but worse passibility all over. Good for casemates/arty and slow turning tanks (T67 hellcat, grille T95 etc) Smooth Ride: This skill is hotly debated. If your tank has more than .25-.27 dispersion on Forward movement (W key only), it's worth getting early. otherwise, its only use is to counter Clutch Braking's increased dispersion. (more deg/s = more bloom) get if after ORD and Clutch. Look up your favorite tank at Tanks.gg in the stats or compare tabs! Preventative Maint: Great for preventing engine fires (not gas tank fires). Stacks with Auto Fire Ext! Training the crew on FireFighting is a good idea as well if you plan to run Food instead of AFE. Controlled Impact: Only for teh lulz if you like ram kills (KV5/E50M hate train) and maybe Cromwell blitzing in SH. Hilarious but not needed.
Loader: Safe stowage: best loader skill. +25% durability to Ammo racks. (ammo rack HP+25%) Stacks with the wet ammo rack equip. Spreadsheets to look at Adrenaline: Useful if you are consistently below 10% health. Obviously of limited usefulness, but you can win a reload fight with it. Intuition: lol no. of very limited usefulness even if you change shell types A LOT. and there are times where it might screw you over.
Radio Operator: Situational awareness: +3% to VR. the ONLY useful skill the RO has. if you aren't training this, train camo/repairs/bia/firefighting before anything else. Call for vengence: Useful ONLY if you are in the habit of suiscouting. otherwise its a waste. Relaying: lol no. Signal boosting: see Relaying.
When figuring out the skillset you want to have, it's always important to consider the playstyle of the tank and how many available slots you have for crew skills. What are the weaknesses? what are the strengths? how can I improve this tank with my skills? This is the 'tactical' sense of crew skills.
I always consider where I want this crew to stop at on the tech tree (tier 6/8/9/10) and think about what that tank needs as well then build towards that in an efficient 'strategic' sense. Any time the Tech tree forks, I always consider if it's a change in class (light to med, med to heavy) and if I want both branches or just 1 and if I can use a premium tank to develop both sets of crews.
There are some tanks (meds) I prioritize immediate surviveability on (repairs/plznoenginefire) and others where mobility (Lights/heavies) and accuracy are the order of the day (Primary combat skills, passive combat skills).
For pretty much everything it starts with Camo/Repairs, BIA, then Vision/accuracy skills. Consider the tank and it's playstyle to make the right picks. Verify on VBAddict.net or just start there.