I then import those pdfs into paperwork in bulk. It has a label system and learns to apply labels correctly, which isn't 100% accurate but rather helpful. It also has rather quick fulltext search, which is nice. All in all, paperwork isn't perfect but it does the job well enough for me.
As a scanner, I got an Epson ES-200 (DS-310 in Europe) from Amazon Warehouse Deals (the packaging was dinged, which apparently justified a 35% discount).
I keep around the originals in a big chronological pile, rotated yearly. If I ever need an original document, I can search for it in my digital archive and find out its date. Then I can binary search for it in the pile.
The annoying part is scanning all your old stuff. Even with a fast feed scanner (mine is about as fast as Tesseract can process it in simplex, and twice as fast as the OCR in duplex, making my CPU -- and not the scanner -- the limiting factor), it just takes a lot of time.
To store the files on disk I keep directories marked by topic/year/month/day. The topics are stuff like taxes, finances, bills, etc. The important documents are in a couple encrypted HDDs that I use for backups. I've been thinking of doing an offsite storage like Backblaze B2 but it's probably overkill.
After scanning stuff in, everything gets shredded. There usually aren't many things to save but once they've been scanned they're there forever.
[0] https://www.amazon.com/Fujitsu-ScanSnap-iX500-Duplex-Scanner...
I'd love to do this as well but I'm sure at some point in the future I'll hear "sorry this won't do, we need the original".