This is the gear that is known to work, we can help you determine what will work for your budget/ministry.

Cameras:

Sony Compact Remote Control Tripod [$130]
https://www.bhphotovideo.com/c/product/913251-REG/sony_vctvpr1_remote_control_tripod.html

Sony HDR-CX455/B Overview [$400]
https://www.bhphotovideo.com/c/product/1211907-REG/sony_hdrcx455_b_hdr_cx455_full_hd_handycam.html?sts=pi

Or Canon XA15

Encoding:

For encoding like the Datavideo NVS-33 record deck/encoder this is a standalone device that a computer is not required.  [Approx. $700]
https://www.bhphotovideo.com/c/product/1472026-REG/datavideo_nvs_33_h_264_encoder.html

JTech H.264 hardware encoder. [$200]
https://www.amazon.com/gp/product/B0761X6L3C/

Or you could use a capture card like this. [Approx. $150]
https://www.amazon.com/Blackmagic-Design-DeckLink-Recorder-Capture/dp/B00CDIXCSO

Or a Magwell SDI or HDMI capture card.  Note: this takes usb 3 to work correctly. [Approx. $300]
https://www.amazon.com/Magewell-Capture-Video-Dongle-XI100DUSB

Elgato Game capture
https://www.bestbuy.com/site/elgato-game-capture-hd60-s-black/5187800.p?skuId=5187800

Note: for the Blackmagic, Elgato, or Magwell you would need a computer running vmix, obs, or wirecast (RTMP encoding software).

Advanced setup:

We would suggest getting a switcher.

These are the 3 models that we prefer Blackmagic ATEM HD [Approx. $1000]
https://www.bhphotovideo.com/c/product/1318041-REG/blackmagic_design_swatemtvstu_hd_atem_television_studio_hd.html?sts=pi&pim=Y

* The pros of this switcher has SDI/HDMI.  Also has an auxiliary output and a multi-view / preview.

Atem Mini Pro
https://www.bhphotovideo.com/c/product/1557461-REG/blackmagic_design_atem_mini_pro_hdmi.html
* Pros: has preview out, record, & stream option.

Or The Blackmagic  ATEM MINI [Approx. $300]
https://www.bhphotovideo.com/c/product/1507214-REG/blackmagic_design_swatemmini_atem_mini_switcher_control.html?sts=pi&pim=Y
* Pros: low cost switcher, Cons: no record or multi-view / preview.