Hi Percy,
Welcome to the electric forum. A drop in plug and play power system is easy for the Strega, but the learning curve is not so easy. My recommendation is to decide on a power system and ask questions as they arrive while working with it. There are many helpful people here that will help prevent rookie mistakes. Read some of the old threads in this forum, they are a great resource.
I will start by saying a 4S setup will not fly the Strega. Also, if you were to use a 3300mah battery you would also have 2475mah-2640mah rather than 2200mah. It is safe to use up to 75%-80% of the capacity.
Here is the power system that flew Paul Walkers 750sq" Impact at 75oz.
Motor: Plettenberg Orbit 30-12 (10.75oz)
Battery: Thunder Power 5S 4200mah Pro-Lite (16.5oz)
ESC: Schulze Future 18.46K F2B (1.75oz)
Timer: Proprietary
Here is the power system that flies my Mustang, 675sq" and 68.75oz.
Motor: NEU 1907/2Y (9.5oz)
Battery: Thunder Power 5S 4000mah Pro-Lite (14oz)
ESC: Schulze Future 18.46K F2B (1.75oz)
Timer: Z-Tron V.4
Here are several other options that will fly your Strega well.
Motors: Hacker A40-10S or A40-12S, Plettenberg Orbit 25-14, Quantum 4120/06, Rimfire 50-55-650, Turnigy TR50-55B-600, AXI 4120/14, NEU 1910/1.5Y
Batteries: MaxAmps 4000mah, TrueRC 4000mah, Kokam 4000mah, Fullymax 3700mah
ESC's: Castle Creations Phoenix-45HV, Jeti Spin 44
Timers: JMP, Z-Tron, Hubin
As you can see there are MANY power systems that will work. Ideally the Strega will be ~45oz or less before the power system is installed. This should give you a takeoff weight of 75oz or less which very close to your current takeoff weight. This is be a lot to digest, so please let us know if you have any questions.
Mike