Here's a video about why I started wet shaving. It does give you a better shave, but the main reason I made the switch is for the cost. Here I explain how I got started wet shaving, and what you will need to get started. I won't give you a ton of options, since that can get confusing. I'll just tell you what I bought. If you do the same, it's a great starting point.
The short story is: It'll cost you about $50 US to get started, and the only ongoing costs are soap and blades, which are super cheap.
Here are the links to everything I talked about in the video:
How to Shave in 120 Seconds: https://youtu.be/38Sz1QxjQwk
Merkur 34C Razor
Prorazo green soap
Astra Superior blades (100 pack)