raidz1 is the equivalent of raid 5 - It'll use all the disk's space, minus one for parity, your 4x2tb disks will give you 6tb of usable space and allow for one disk failure at a time. zfs is independent from freenas, and zfs is 'basically' a software raid and filesystem all in one.
If you decide to use zfs, it doesn't really matter if you use your onboard controller or your external card - as long as you can turn the raid feature off and simply pass through the disks to your system (this won't be a problem for your built in controller, you'd have to double check your card supports this).
I'm a big fan of software raid over hardware (and even more so of zfs over both), but honestly think you'd be best off using what you're most comfortable with. The biggest drawback of zfs for most 'normal uses' (especially on a forum like this) is expanding your array in the future. zfs requires careful planning and bulk purchases of disks to maintain performance and redundancy, while your other options probably allow simply adding a disk at a time, growing the array without a second thought.
Only you can decide the level of redundancy, which strongly relates to the usable space available. If you're going down the zfs route, you need to regard it as a 'fun project'. As much as a die-hard nix/zfs fan I am, there's absolutely nothing wrong in running windows 7 using a software raid or your LSI card. Fully checksum'd data, bitrot protection, snapshots etcetcetc is great, but it also won't make or break your media storage solution. Also, completely unrelated - my own silly opinion is that media storage is relatively disposable
I wouldn't worry about sata II/III differences - If you've got a 'large storage' disk that can realistically throttle the bandwidth of your controllers, can you nip round my house in your time machine and give me next week's lottery numbers?
There's a few threads on unraid too - Another solution to consider and stress you out
That provides a nice simple solution to a growing media collection, providing redundancy and easy expansion.