This is the gear that is known to work, we can help you determine what will work for your budget/ministry.
Sony Compact Remote Control Tripod [$130]
Sony HDR-CX455/B Overview [$400]
Or Canon XA15
For encoding like the Datavideo NVS-33 record deck/encoder this is a standalone device that a computer is not required. [Approx. $700]
JTech H.264 hardware encoder. [$200]
Or you could use a capture card like this. [Approx. $150]
Or a Magwell SDI or HDMI capture card. Note: this takes usb 3 to work correctly. [Approx. $300]
Elgato Game capture
Note: for the Blackmagic, Elgato, or Magwell you would need a computer running vmix, obs, or wirecast (RTMP encoding software).
We would suggest getting a switcher.
These are the 3 models that we prefer Blackmagic ATEM HD [Approx. $1000]
* The pros of this switcher has SDI/HDMI. Also has an auxiliary output and a multi-view / preview.
Atem Mini Pro
* Pros: has preview out, record, & stream option.
Or The Blackmagic ATEM MINI [Approx. $300]
* Pros: low cost switcher, Cons: no record or multi-view / preview.