I use an Iriscan portable/receipt scanner.
See the models at Amazon
The lowest-priced option is $110. (Mine was $75 refurbished from a Woot.com sale last year.)
Flatbeds take took long, and flatbed scanners err on the side of quality vs speed. A receipt doesn't need quality, it just needs to be readable for records purposes. So a portable scanner errs on the side of being fast.
The downside to a receipt scanner is that it costs the same as a higher-quality scanner. But you're paying for speed, portability, and ease of use. It comes with a soft leather pouch, and is about the size of two corndogs (on top of each other, not side-by-side). For that reason, I often take it with me on trips, just in case I need a scan of something. It does have a "high quality" mode, but it's nowhere near as good as a flatbed. I think of it as a receipt scanner, or with slightly a better mode for emergency on-the-road scanning needs.
I tried to be cheap and use my flatbed for scanning receipts, but quickly became disgusted with how slow it was.
Scanning receipts is a good idea, because the paper fades after about a year. (There's no "ink", it's thermal changes in paper itself that create the writing on a receipt. It lasts maybe 2 years max before it's so faint that it can't be read anymore. That's awful for anybody needing to keep tax records for the prescribed 7 years.)
You can't avoid paper. Buy a file box and some folders from Walmart (cheaper than the office supply stores). Scan what you can, keep hard copies for recent and/or more urgent documents. I only scan something after it's more than 3 months old, excluding certain personal tax records (receipts groceries or going out to eat, for example).