Consumer-grade NASes always use software RAID, and generally it's a semi-proprietary type that they don't refer to as RAID based on Linux mdadm for management. It usually provides many more options for configuration than simple RAID levels, but simple mirroring of two drives is possible and more than enough for home users if the storage capacity is enough. A RAID5 array is also fine with 1Gb Ethernet as far as being able to saturate the link, but RAID10 is more reliable and faster in operations other than transferring over the network (like if you decided to run virtual machines or other apps).
The OS on those devices is Linux-based. This may be partly why there aren't any Wi-Fi versions, as Wi-Fi support in Linux is not super and it would make them cost more to develop and support, along with there being little desire for Wi-Fi adding to the hardware cost. Most people who want a NAS want it to be fast and reliable, and that's only going to be assured with a wired connection. Even a 100Mbps Ethernet network is going to be better.
It's likely possible with some NAS models to add your own Wi-Fi. If it has a PCIe slot you can use that, or USB, but you'd need to know what Linux distro the OS uses and verify what models of Wi-Fi adapter are most compatible, and figure out how to manually install the drivers and add the interface. Linux has limited support for models mainly because of the chipsets, where the manufacturers don't release open-source drivers or binaries that can be added to Linux easily. As such, they are often limited to the 2.4GHz band even if you have a super-fast 11ac adapter, so you end up with a 150Mbps connection, maybe 300, compared to 1000Mbps with 1Gb Ethernet. And that's only max theoretical Wi-Fi speed, where you'll really get maybe 80Mbps, but you get 900+ on Gigabit Ethernet. Each individual PC will be limited to the speed of its own connection, of course, but if 3 PCs that have a 600Mbps Wi-Fi connection all try to download from a NAS with a 150Mbps Wi-Fi link, everyone will be screaming at each other. If it's got 1Gb, 3 of those PCs might not even notice that there is anybody else doing anything.
As to being able to "grab and go", you should have a USB hard drive connected to the NAS to perform backups, which you can grab in an emergency to save the data. There are likely many more important things you should be trying to take than ensuring you get the physical NAS hardware. But a power cord and single Ethernet cable isn't exactly a lot to unplug.
You also don't seem to be fully informed about how a NAS works. There is no software configuration EVER required on the individual PCs when accessing a NAS other than opening the share. It's all transparent - all the PCs see is a shared network folder, not a disk. Disk configuration is all done on the NAS. Technically, you could configure them using iSCSI, with individual volumes created on the NAS which each PC connects to and sees as a "disk", and then perform software RAID on the PC, but that would be a ridiculous amount of configuration for a home, create an enormous amount of additional overhead, and be quite stupid.
There are plenty of recommendations and reviews available online for a specific NAS model. You may need to dig deep if you want to try adding Wi-Fi to one.