My perfect ops dept would start with getting the right people with the right attitude. Experience is essential too. You need some folks who've been around to mentor the ones who haven't. Find a couple of these guys and pay them well n treat em right, they're worth their weight in gold.
You shift pattern will depend on your ops but if you need H24 coverage and are not limited to duty times (as with FAA) then 4on/4off works well.
The systems for crewing and flight planning, well that depends on your budget and the more you spend the more you get. Do your research, there are alot of new products out there at good prices trying to get a foot in the door.
As paperless as possible is the way to go. Make sure what ever systems you get can talk to each other.
Just my thoughts...