Technically yes, if your board supports onboard RAID, you could just put in hard drives and RAID them directly and store directly on your computer. However, this isn't always the best strategy. I recommend offloading. This means take the work and the protection of your stored data out of your daily work computer and place it in a computer or device dedicated solely for that task. First, this will make things more efficient for your storage, as it's centralized and can be protected with higher-quality RAID in a high quality NAS, and second it can be more protected from "daily usage dangers" meaning risks of viruses on your normal computer or possible deletion or corruption. I've also seen quite a few onboard RAID controllers corrupt or lose RAID arrays, so I would not use it for your primary storage. I only use onboard controllers for RAID 1 arrays now when they aren't storing data really, but when they needs always-on capabilities, where they must have access to the computer even if one drive fails. It's not intended as a backup, which I've seen a lot of people set up and do.
There are a ton of options for storage out there, as you know, but the key really is to begin with offloading the storage to a centralized point specifically designed and handling just that task.