Full disclosure: I haven't done any serious work with video. Just some university projects and stuff. I am by no means an expert.
- I have heard good things about Blue Microphones.
http://www.bluemic.com
They seem to have a lot of products aimed at vloggers and podcasters.
- I am currently using Adobe Premiere CC for my video projects, as I get a student discount. Before using that, I used Sony Movie Studio Platinum.
http://www.sonycreativesoftware.com/moviestudiope and I found it to be pretty robust for consumer software. It might be good enough for your needs, and there are free trial versions for download.
- In terms of cameras, I use my Sony a5000, which is more geared toward photography. It's decent for video, but you would get better results probably with a dedicated video camera, and I don't know too much about those.
- Getting a tripod is great, but you also may want to think about a "steadycam rig" if you intend to move around while filming. Ready-made ones can cost a ton, but I have seen friends make some pretty cool homemade rigs that keep cameras steady while moving.
I hope this helps a bit. Good luck with your videos!