I worked there for 3 1/2 years, but it has been over 5 years ago. Like Rid mentioned, it is a very busy system. They cover "downtown" Indy. The outlying townships have their own fire-based ambulances, for the most part. IFD does have a few ambulances on the north/east side of town, but that is because the townships merged with IFD.
Wishard is the county hospital, as well as a teaching hospital. It is a level I trauma center and has the only adult burn unit in the area. There are alot of great docs there, as well as nurses and other associated staff.
When I worked for the ambulance service, they ran medic/EMT trucks, but are going to dual medics now. EMTs that were already there before the change still have their jobs, but as they leave the plan was to replace them with medics. I haven't heard lately if that is still the plan though, so I could be wrong about that. I haven't had a chance to talk to anyone that works there recently.
Public safety in Indy is going through changes. A couple years ago, IPD and Marion Co. Sherriffs Dept. merged. It wasn't exactly as smooth a transition as it was supposed to be, and there are still growing pains within the police department. The merger of those two departments was looked at as a "trial run" before attempting to merge all of the county's fire/ems into a single department. Legislation has yet to pass that will force that to happen, but a couple of the townships have opted to go ahead and merge before they are forced to do so. I mention all of this because I am not sure what it all means for Wishard ambulance service. I have heard various rumors, including the hospital maintaining ownership/control of the ambulance service and IFD taking over the ambulance service and running it.
At one time, I would have said that Wishard was "the" job to have in EMS in Indy. It was very difficult to get on. You really had to know your stuff, be confident, have excellent references, etc. People would apply 4 and 5 times before getting a phone call for an interview, and would typically have to go through a couple hiring processes before actually getting offered a job. That isn't really the case anymore. It is still definately one of the better places to work when it comes to pay, benefits, etc, just not as difficult to get hired there anymore.
It has been too long since I worked there to be able to really tell you much about current benefits. Sorry I can't be of more help in that area. As far as a work schedule, they work 12 hour shifts on a rotating schedule (Mon/Tues - on, Wed/Thurs - off, work the weekend. The next week you work the opposite of that.)
You might also want to consider looking at IFD. I am not sure if they are hiring civilian EMS anytime soon, but everyone I have talked to that works there is really happy with it. They work the same schedule as the firefighters, so 24 on, 48 off. I know the medic pay is decent, and if they have the same benefits as the firefighters, they are pretty good as well.