Good replies here, but I’ll thrown my couple of ISK into the pot.
E-war is a support role, and so highly dependent on what your Fleet Commander needs, or expects to need, in terms of support. It will fall into one of three areas:
Tackle. Webbing, Warp Disruption and Scrambling - basically stopping a target from escaping - pinning them down for the kill. This is useful - you fly a fast ship, get in close and try to avoid being killed. Train up the propulsion jamming skills and the navigation skills.
Often the point in catching other players for the fleet to kill. Limited value in PvE fleets - though webbing is always useful!
Logistics. Remote Armour Repair, Shield Boosting, Capacitor feeding if required. Working as part of Team keeping the fleet alive and fighting. Always valuable, lots of team work and useful in PvE and PvP fleets. A dedicated logi-pilot can be skill intensive, and will be busy in a fight.
Electronic Support - traditional E-war aimed at degrading the enemy’s ability to fight. Situationally dependant - so confirm what is needed with the FC. Sensor attacks, ECM and Damps are good for disabling enemy logistics or disrupting enemy damage dealers. Tracking and Missile disruption is good for defanging an enemy. You know if you are getting it right when people are trying to kill you. Then you start the dance of bouncing around at range and generally causing problems. The FC who trusts you will give you a lot of freedom, but you need knowledge of what works against what and how to survive. Good in PvP fleets, much less so in PvE.
Finally there is Neuting (fourthly, but it never feels like e-war) as it’s high slot and engineering stuff) - crippling a target’s capacitor. Effective, but you again need knowledge of who it works against (logi) and how it works. More or less exclusively PvP
Good articles on Eve University for all of this.
In general a good E-war ship, especially a disruptive trouble maker, can be cheap. The T1 e-war frigates are all well bonused and often better than more expensive ships. A specialist Crucifier is less than 10m ISK with T2 fittings - and rarely does a ship feel so well named! Fragile, so arrive fashionably late and keep at range, but they can be devastating. Serious Logistics are the realm of T2 Cruisers (not cheap and often corporate assets), but a T1 logistics wing is a good place to learn.
Talk to your corporation, see what they need or how you can help and jump in.