The strategy of Edge of Darkness is largely about managing the balance between short term challenges while keeping longer term goals on target.
Here are some things to think about. These are not hard-and-fast rules, and depending on the set of 10 locations in your particular game and what advancements you observe other players choosing, you should consider adjusting your strategy.
Always sleeve advancements on your own cards if possible rather than Neutral cards or other players' cards.
Early in the game, when drafting, try to get exactly 1 of your own cards in your hand so that you can sleeve on it. Skip other cards that are yours so that you will get them next turn.
Short Term Problem Solving
All advancements you sleeve can be used right away. Use your once-a-turn sleeve to adjust to immediate problems; out of money, out of Agents, about to be attacked by a threat, etc.
Long Term Planning
The counterpart to #3 is that all advancements you sleeve (especially early in the game) are investments in future turns as those cards will continue to cycle back to you.
So if there is not an immediate problem to solve, make a long term setup move; claim Allegiance, dispatch Agents so you are ready to hunt threats etc.
Analyzing The Setup
Survey the set of 10 locations looking for a few things:
How Agent intensive is this setup? If there are 7 or more locations that require Agents, you may want to sleeve a advancement early.
However, if you see all the other players doing that, you can probably get away with using their cards and make a longer term setup move instead.
How Coin intensive is this setup? Are there multiple effects that require Coins? Is there at least one easy way to get Coins?
Are other player sleeving advancements that generate more than 1 Coin?
How dangerous will the threats be this game? Pay attention to how many Threat cubes are indicated on the advancements that players are sleeving.
If all, or most of, the advancements players are sleeving have Threat cubes on them, expect a lot of cubes to be going into the tower by mid game.
Defending Against Threats
Failing to defend against threats can rapidly start to cost you lots of Victory Points. Not only do you start losing points on the Defense track, but you also miss out on gaining 1 Reputation for each successfully defended threat.
Overinvesting in defense however can mean missing out on building an engine. The key is to remember that no matter how big a threat is, it only knocks you down 1 spot on the Defense track.
Think about investing in advancement early so you can defend against the small 2 and 3 Damage threats. If you only ever get hit by the big threats, you are defending efficiently.
Lots of points can be scored by hunting threats efficiently. Generally killing a few big threats rewards you with more than killing lots of small threats. However, getting a lot of Battle Strength all in one turn usually takes planning.
Think about grouping contacts on the same card so you can be sure to get those effects at the same time.
Also, some like to say the best defense is a good offense; killing small threats can be efficient if you are picking them off before they attack you, but don't bother killing a small threat if it's unlikely to attack you unless you can do so for little or no cost.