I forgot skills! Thank you. How would you change it to cover a bit of longer range support?
For your skills it's best to focus on mobility and agility
AGILITY
Cat fall. Only really useful if you plan on spending a lot of time jumping of tall buildings.
Clamber. Only useful if you spend a lot of time scaling tall buildings.
Might leap only useful if there are a lot of gaps to leap across (like tall buildings, is Agility the Spider-Man skill tree?)
Dodge. A 6+ save that you can take in addition to other saves plus can move out of Blast and template hits. (Still Spider-Man...) OK that's pretty decent but it's is more of a second skill choice because of...
Spring up!
From being pinned pass an initiative test (on your great Esher initiative) to stand up for free and carry on as normal. This really keeps your top fighters moving and should they get shot before they activate they gain the benefits of being pinned before they act. Those Nerves of Steel Orlock and Goliath chumps still standing up so their foes can still shoot them.
Sprint. Ever want a Death Maiden legging it around the battlefield faster than a Waster's Dirt bike? (A triple 6" is 18" of movement with a couple movement upgrades a death maiden can top 24") There is no better way of repositioning your heavy hitters.
(Seriously is Agility the Spider-Man skill tree?)
COMBAT
Combat master. interference and assist rarely comes up. Not enough multiple model combats.
Counter attack. In reaction attacks you can make additional attacks for each one your opponents miss.
Unless you can practically guarantee a kill with your reaction attacks you should be using your great Esher initiative to withdraw and keep moving. Esher are kind of like boxers with glass jaws. They hit hard but lack prolonged slog staying power. If you are in the situation where you get a lot of Counter Attacks it is likely that your foe is tougher than you and will hit you harder in prolonged melee.
Disarm. A alright skill but is best used on weapons with Disarm already. The chain axes but they are only on the Queens list otherwise you need Trade post access to fully realise this skill. Also the skill can be entirely useless against foes with no Melee weapons.
Parry a legitimate good skill. Even better with swords and the like. You will get better use out of your Stiletto swords with it.
Rain of Blows. Outside of Overseer you only can actually make use of Fight (Simple) in multiple turn combats. Pronged melee is not Eshers thing. Stick and move. Stick and move.
Step aside. Use your great initiative to cancel an attack. Couple it with Parry and a sword and it makes you very hard to touch in melee. Now this is a potential combination but is quite XP intensive especially if you add counter attack to the mix to potentially turn three hits into misses maximising your Counter attack potential.
Most of the Fineness skills focus on mobility either allowing you into harder to reach places via your charge and move actions, benefiting retreat actions letting you move around close combat better or making your move actions more Versatile.
To get back to your original skill question for longer ranges support, your best bets are skills that let you get into firing positions faster or keep active while there.
The rest of your good skill access works best getting into and out of Melee.
FNB <- how about this? Save up for chem alchemist and some arrows next, or drop chem thrower on specialist for needle rifle and invest now?
I would go needle rifle over chem thrower. Its cheaper, freeing up credits for more sisters, it is blissful immune to the Gas defence of Respirators, even if it does not harm any one in a hit at least it Pinned them, had good Special weapon AP (only melta have better). It also has decent range for a Silent weapon when sneaky attacking.
It being a lot cheaper let's you get comfy with Alchemy earlier as well.