My goal is to create an simple offsite backup of my CasaOS setup using a RasPi 3b+ with external USB drive at a friend’s house. Are there any recommended methods for doing this?
Also: what should I look for in an external hard drive as far as reliability goes for something that will essentially always be on? I’m not well versed in all the WD blue, red, etc. Does it matter?
Flash drives are notorious for spontaneous and ungraceful failures. At the very minimum, you want a proper Hard Drive or SSD. Generally, any reputable brand marketing a "NAS" drive is probably what you want. Nothing spectacularly fast, but designed for a lot of power on hours.
One important thing with SSDs is that many even today aren't great with power loss detection.
Kingston makes a very reasonably priced data center class SSD with lots of RW cycles and specific power loss protection. I haven't tested them yet, but it's a good sign they at least mention it in their specs. I previously used intel data center class SSDs, but they're harder to get ahold of these days.