Get a Canon C100 Mk2 if u want a real video camera...Get a GH3 or GH4 if u want a DSLR...As far as lenses go....get a fast 50mm prime and thats it (or a 25mm prime if you go with the GH3/4).

I second getting an actual video camera...the c100 (mk2 !!! ) is indeed an excellent choice
I also second Aputure's LED lights. I suggest getting at least 4 lights...3 light the talent and you have 1 for lighting the background.
Get some type of reflector or bounce board if you're shooting outdoors in the daytime.
Get the Sigma 18-35mm Art lens, and a fast 50mm Prime. Better than the 24-105 for low light situations...
For audio check out the Rode Link wireless and the NTG-3 shotgun (get a blimp for it and a boompole with internal coiled cable). If you need to record more than 2 channels of audio (or want WAY better quality than what the C100's preamps will provide) look at the Sound Devices 744t...expensive but worth it.
Get a solid tripod...I own this and its been problem free for nearly 3 years now http://www.bhphotovideo.com/c/product/861089-REG/Libec_RS_350RM_RS_350RM...

As a MFT camera I can fully recommend the Voigtlander Nokton lenses...The 10.5mm would cover your wides...the 25mm for normal...and the 42.5mm for tight shots...Consider if you're going to stick with the MFT format though.

Lighting a scene for a multicam shoot...2-3 cameras.

Altiverb 7 (made by the same guys who make Speakerphone 2) also has really cool features that can match the acoustics of a production space using the sound of the slate clapper...

another consideration is to use the same preamps that were used on set...every preamp imparts a different "flavour" so to speak...so i would bring the same recorder used on set into the studio and run the mics through that instead of the studios preamps (especially if its a studio primarily focused on music, as their pres are more than likely very coloured in tone...post guys need clinical preamp sound...too much colour is bad)