Sure, that’s what RAID is designed to do. However, I’d suggest also looking into what happens when your array is degraded and how to rebuild it.
Fast reads
I’m a bit surprised you need fast reads with a media server. You’re probably going to have to clarify your needs a bit more.
Easy plug and play expansion
Since I’ll have 8 drives (or 6, if I use the smaller server, it would be nice if I could swap out one of them without losing data and add a larger one, which would then get used automatically. Is that something that RAID is good for?
Standard RAID levels generally don’t have options to add larger drives. I’m not sure what you mean by “plug and play”. I’m pretty sure almost all setups will involve a fair bit of configuration.
I’m hesitant to set up backups because it’s going to be a lot of data.
It’s also a lot of data to lose if things go more wrong than you expected (multi-drive failure, bit-rot, etc.).