I am no photographer, but two that I recall seeing others discussing here on the forum are the GoPro and Mobius cameras. Both brands have several models and I don't recall which ones everyone was talking about? They are small and will fit on our trains for making the 'engineer's view' type videos.
I did a search on each one (links below) for the things others were saying. As I recall there was a Mobius model for a very good price that gunrunnerjohn got and I believe he was pretty happy with it. I think it was maybe $30-$40 or so, but I really don't remember the price.
I have a Fuju F-500 that I use for taking pics of my trains for inventory and I also fool around with it taking layout pictures and videos, My grandson also uses it here for the same purpose. I think he does a much better job than I do. I warned you I was no photographer! He also has a GoPro I got him for Christmas, but he hasn't yet brought it over to take any train videos.
Anyway, here are the links to some threads that may offer more details. Mobius Posts - GoPro Posts
Hopefully some of the folks using these things will be along to comment as well.