I will suggest to stick to popular platforms like Youtube or Facebook for Live webcast. Though you can choose any other established platform as well.
Own server will put you into more cost.
DSLRs don't support live video to be streamed. Though if you are planning to shoot, process and publish; mid range DSLRs are good options.
For Video,
For Audio, get a good microphone; en.rode.com/microphones/video. In addition, you can have a collar microphone; just to be on safer side with Audio.
Lighting is always good, have at least 1, good to have 2. Keep the lighting consistent.
Use either Premiere or Final Cut or any other tool. In my opinion, one is enough.
Once published, content promotion is the key to gain more traction.
P.S. Be careful about the content and the length of the video/webcast.