Yes it can be done on a budget, although the more you get into it, the more alluring the expensive stuff is.
Even without a license, you can get started with some listening only stuff. For me, I picked up an rtl-sdr off Amazon for pretty cheap and started listening to NOAA weather satellites.
Before you start transmitting, you'll need to get your license. Hamstudy.org is a great place to start practicing for the exam.
My idea was intentionally unrealistic and meant to represent an extreme. Your suggestion isn't just realistic, it already exists. Admittedly, I'm not really that interested in operating a landscaping company, I just want eliminate some of the unnecessary noise noise.
No.
After reading this question, I got strangely excited the thinking I had a relatively older and/or unique experience. Nope, most all you guys are as old as me. Late 90's, early 2000...got a red hat CD in some literature...installed it. Now only use Windows if I need to for work which I haven't needed to for over a decade.
I had no idea this was a thing. Yeah for having friends who don't make a big deal about trivial shit.
Not sure how much money that is, but I would start a "quiet landscaping" company that used reel mowers instead of gas mowers, rakes instead of leaf blowers, and I would undercut every landscaping company in my town just to promote the idea of a quiet neighborhood.