In terms of hosting, I'd definitely recommend YouTube. You'll have less technical limitations to help you reach that broader audience. YouTube just makes it really simple to send a link for people to watch the video from any device. Plus added control of things like the privacy of who is able to view the videos, have access to stats to see which videos are being watched the most and can even create video playlists if you want to share just one link to give access to multiple videos around a specific topic. You also can allow volunteers or fosters to leave comments & questions on the video that future viewers can also see. If they're asking the same questions, it'll help to save you time there too!
For equipment, a microphone is definitely beneficial if you plan to do a lot of videos and want to maintain consistent and clear audio. But I've also successfully recorded videos with a good pair of headphones that have a quality microphone built in. With headphones I usually just do a variety of tests in different rooms and playing it back to hear which room had the best "acoustics" using the same equipment.
Either way, recording these as videos sounds like a great idea and will totally help you save some time! Happy recording!
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