I'm not a particularly good Blitz player, but I've been doing enough min-max powergaming in RPGs to learn a thing or two about skills/abilities/perks.
Skills in Blitz can be broken down into broadly three categories: permanent, conditional and chance-based. This is also the order of their general usefulness. A permanent skill offers a constant bonus in a particular area, a conditional skill requires a particular situation for it to become active, while a chance-based skill activates more or less randomly based on its chance percentage.
Regarding reseaching them, there are two schools. One school tends to perform research blitzes (heh) in the most useful skills in each branch (usually the permanent ones) in order to have flat bonuses across all their tanks. The other school goes for a marginally less overall-effective but more balanced approach, by researching all the skills in a branch to a given level (first the permanent, then the conditional, finally the chance ones) before going for the next.
Now for the skills themselves.
Light tanks:
- Hasty Shot: chance-based. Most useful when doing unaimed snap shots or drive-bys. The target needs to be highlighted by the targeting chevron (and evidently inside the aiming reticle). Useless when deflection shooting (blind-firing in front of a speeding tank). A KV-2 player's most valued skill. 
- Breakthrough: conditional. It's mostly useful for getting a light or fast med out of trouble, if it bit more than it can chew. Also useful for tanks like the turbo pancake (AMX ELC) or the Littlepard who are drive-by machines.
- Soft Recoil: conditional. Useful mainly for autocannons, clip-loaded guns and generally guns with largish post-shot bloom and high RoF.
For research, Breakthrough or Soft Recoil (either of them first/second) followed by Hasty Shot.
Mediums:
- Rage: conditional. Pretty useless when paired with an autocannon or clip-fed gun. Best with a derp or generally high alpha gun.
- Pen Boost: chance-based. After the change to pen values it has become less useful, since now the standard interval is narrower (85%-115%, instead of the previous 75%-125%).
- Mentor: permanent. This is a metaskill: higher levels in it allow you to research all the other skills quicker, since you earn more crew XP from battles. Not as critically important now that you can exchange elite XP for credits, but still very useful.
- Smooth Ride: permanent. This decreases dispersion during vehicle forward/backward movement. It's obviously useful for turreted tanks (who can point their gun in one direction while driving in another) doing peek-a-boom or sidescraping. Great for those "damage/destroy an enemy tank while on the move" missions.
- Smooth Turret Traverse: permanent: Again, primarily useful for turreted tanks doing snapshots or deflection shots. Also useful for turreted TDs and somewhat useful for casemate TDs with wide gun arcs.
These were the first skills I've begun researching when I first started Blitz (on account of me picking the Med Mk.I as my first tank, a bad choice). I've gone Mentor -> Smooth Ride -> Smooth Turret -> Rage -> Pen Boost (although I can see the merit of swapping Ride with Turret).
Heavies: note that all the skills require a specific situation for them to be useful.
- Robustness: conditional. Requires you to take module damage and not repair it. The penalty reduction starts getting pretty significant at higher levels, although generally it's better to just hit the Repair Kit if/when you have 2+ yellow modules (or when your fuel tank/ammo rack get yellow, for extremely obvious reasons) unless you really want one of the clunker medals.
- Close Combat Master: conditional. Anti-CoD skill. When coupled with cumulative turning (turning both hull and turret at the same time), higher levels can give you an edge against somebody trying to dance around you.
- Firefighting: conditional. It's less vital than it appears at first glance, since it only increases the crew's firefighting speed. Whenever you catch fire, it's better to just immediately hit the Multi Kit (if you don't have Auto Extinguisher). Useful primarily when your Multi Kit and/or Auto Extinguisher are on cooldown and you're unlucky enough to be set alight again. High levels provide a sizable decrease in fire duration, but the hitpoint loss during even a brief fire is severe.
- Adrenaline Rush: conditional. Makes your tank more shooty when you're nearly dead. Can provide an edge in that final 1v1 of the match.
- Repairs: conditional. Depending on how many threats are in your immediate vicinity, you might sometimes choose not to pop your RepKit/MultiKit if your tracks get blown (especially if you also have high Robustness). Stacks with Protective Kit (which gives a flat +10% to repair speed).
I went Robustness first (since I use Protective Kit on most of my tanks), Repairs, Close Combat Master, Adrenaline Rush (one may switch between it and CCM depending on what lines they play) and finally Firefighting.
TDs:
- Sniper: chance-based. I've been rather unlucky with this skill. More than once, I had the icon pop up on a duffed shot.
- Deadly Accuracy: conditional. Very useful for nabbing those Kolobanovs.
When you have both Deadly Accuracy and Adrenaline Rush active, that's when you know Unicum Mode has been switched on. 
- Camouflage: permanent. Not much to say about it, critical for TDs and lights, but all tanks benefit from it (reduces enemy view range, decreases concealment loss after shooting).
- Clutch Braking: permanent. Vital for casemate TDs, but also very useful for heavies defending against CoD-ing enemy lights/meds (stacks with CCM for cumulative turning). Conversely, also good for CoD-ing lights/meds since it allows for tighter turns and reduced speed loss during turning.
- Smooth Turn: permanent. Again, vital for casemate TDs, but useful for turreted tanks as well, especially when also turning the turret (ex. when wiggling). Though shooting while turning both turret and hull at longer ranges is unadvisable since the bloom is cumulative.
TD skills are pretty straghtforward to research. Camouflage -> Clutch Braking -> Smooth Turn -> Sniper -> Deadly Accuracy.
Anybody feel free to correct any inaccuracies or provide addenda.
Edited by N00basaurus, 06 March 2018 - 03:07 AM.