This is not trivial advice :-) Requiring 4 drives in RAID10 has different consequences from 2 drivers in RAID1. Requiring a price < 100$ is different from < 200$. Hacked storage setup (eg. USB drives) versus proper (eg. storage controller with multiple SATA ports) is different.
For example, if you're willing to spend more, but not so much more, than say, 80$, why limiting to the RPi? The Odroid H2, for example, gives a lot of options.
Among the other things, I use it as file server with a COW-filesystem on two (cheap) SSD disks in RAID1. The board has two SATA ports, so it's a solid hardware setup. It has two ethernet ports, so it's ready to work as router. It's also x86, so it will have software support for a very long time¹. And it also runs at an incredibly cool temperature - I bought the fan, but it rarely spins. To be fair though, the H2 cases are expensive trash.
You can certainly do pretty much everything on a RPi4, as much as you can commute 50 km a day with a bike, which is... not ideal :-)
¹=RPi have an enthusiastic community, but ARM boards are second class citizens when it comes to Linux support. While Linux is formally compatible, it's still adviced to run the specific ARM distro.
I did this using an rpi2. It is non-trivial in terms of effort.
In a practical sense the rpi is limited in terms of power to the USB ports, so any build with 2+ HDDs and some sort of wireless USB keyboard and mouse dongle will use up too much power.
In other words, I had to buy a powered USB hub.
I used mdadm to do a software RAID, which more or less worked out of the box but took a while to clone the original drive. Throughput wasn't amazing for anything except occasional pulls and puts; I wasn't going to stream 4K video off of this, though I did have some luck with Subversion and music streaming.
It was clunky enough that I got a Synology box a year and a half later and never looked back.
It's hard to see the advantage over a dedicated NAS device, since the savings on the controller gets eaten up by needing to buy a whole bunch of drive enclosures and power supplies.
This system is going to be set up with software RAID.
I expect to have higher compute power, more RAM, and much better IO throughput than a RPi solution. Also, the laptop battery (which is still good) serves as a built-in UPS.
I can't think of any good reason to do use software RAID, let alone doing so on a Raspberry Pi. I would recommend hardware RAID, ZFS, or a Synology appliance.
If performance is truly not a concern, yes it is possible to do this with a Pi but I don't think you are going to be super impressed.
I looked at NAS appliances, but I think it's still cheaper to create one from scratch (assuming existing knowhow, and "free" time :)
Most would argue RAIDZ is better, but many of these reasons are functionality based over and about just redundancy, i.e. Copy on Write, et all.
Bite the bullet of the cost of N*2 mirrors.
I made a nas with one 3tb drive and zfs. Zfs was a bit difficult to install but now it works really well and the power consumption is low.
You have to use the Linux images mades by ayufan (a third party) though. The manufacturer just list a bunch of distro that run on the cards and most of them seem to be made by some volunteer. I'm not a big fan of that.
It all depends - do you want a fileserver or a crash course in how to build a fileserver?
I have a file server running AMD Phenom II 955 that I'm thinking of replacing with a RPi. Is there a practical way to have RPis manage a software RAID? Performance is not a consideration. Is it even worth looking at RPi in this scenario? The advantages I can think of is small footprint, lower electricity cost.