You can do it like this, i started this way only i didn't had domain-hunter-gatherer i did it all manually with Xenu GoDaddy and free accounts of majestic, lets begin...
Domains
You scrape your own domains, you can get a copy of domain hunter-gatherer and a VPS for one month costing you $77 + $18- = $95
Let's say that you want to build a PBN of 15 domains (start small build it out over time) you scrape yourself 15 domains x$10 = $150-
Content:
I build my PBN's with real content, that means you will be needing at least 150 articles, (10 articles per PBN) make sure that there not all 500 word articles, this content doesn't have to be great when you start out, you can find a writer on here in the BST for $2,50 500 words when you do a bulk order, that means 150x500= 75000 words in many that is $375 in content
Hosting
This is a small PBN so you can if you use $1- hostings and mix them up with your own hosting, it should not cost you more then $100- per year, i know when i did my first PBN i paid about $75 in a year on cheap hosting and divided the rest over the hosting that i was already paying for
So you can start with a budget of $720- for a 15 site PBN...
I did this quickly out of my head so, i really hope i have the numbers straight.
Good Lucxk to you.