When I do DIT gigs on big shows, I like to:
1. Have enough media to make it through a full day. Most productions I've been on don't do this, but it's nice to have the cards as a third backup while the transfer to post happens.
2. Shotputpro with a checksum to two drives simultaneously for an instant backup. The nice thing about shotputpro is that it can transfer to two drives in the same amount of time that it takes to transfer to one. If you go from card to drive1 and then from drive1 to drive2, that will take twice as long.
Most shows will have a big raid on set for the whole show, and then portable drives with enough space for one day of shooting, which get driven back and forth to the post-facility. Most post houses have some kind of big fancy media server, so once footage gets into their system and verified, I consider it safe. But we still keep that on-set RAID just in case post's building burns down or something.
As far as verifying transfers go: shotputpro will verify that what's on the card is now on the hard drive. It does not verify that the footage on the card is right and proper. Every once in a while, a clip will get messed up if the camera shut off in the middle or something. Sooooo, after a transfer is done, I usually dump all the footage into tentacle sync studio and scrub through everything real fast. I find tentacle sync to be the fastest way to do that, with the added bonus of being able to check timecode real fast on multi-cam shoots.
For personal projects, I never do DIT in the field. I just make sure to have enough media for a full day. Then I have a 16TB RAID in RAID 5 at home, dump to that and call it a day. If it's an extra important project, I'll buy a cheapo USB 4TB single drive and double it to that.
I've also set-up some media servers for small production companies, and in that situation, the I've found the cheapest way to do it is find an old iMac or something that they're not using anymore, use that as the server using apple's built in file sharing system (you'd be surprised how well that works). Then get a pair of identical RAID drives, something big, like an 8-bay 32TB. Share one of the RAIDs on the LAN, then do scheduled nightly backups to the other RAID. I used a program called carbon copy cloner for that. It's nice because it will hang onto old files for a while until the backup drive fills up, kinda like how Apple's time machine works. So if someone accidentally deletes a project file or something it can save your ass. There might be a more turn-key solution for that out now-a-days. I set up those systems a while ago, and at the time, that was the cheapest way I could figure out.