Overall, I think going with a RAID would definitely be a step in the wrong direction -- not just because of added complexity, but also because the solution you have in mind doesn't provide you with the `redundancy' you seek.
My recommendation:
(1) Have the internal drive replaced with a 2 TB drive.
(2) Get an external 2 TB drive, preferably a quality drive that allows the drive to spin down.
(3) Then use Time Machine to back up your data onto the external drive. Keep the online backup in addition! Depending on the speed with which you're connected to the internet, it may make more sense to sync only certain files online.
This solution would be about as expensive if not cheaper than getting an external RAID1. It would be faster -- and more redundant.
Now to your post:
Using my internal HD is not an option as I don't have enough space to store my stuff.
Then I'd replace the internal harddrive first and get an external backup drive. This is a much safer option than what you probably have in mind right now: mirrored external drives.
1. I've only got 1 FW800 port so I can only connect one that is "speedy"
You can daisy chain FireWire drives and then access all drives full speed.
2. (The more serious problem) they don't backup automatically and I'm supposed to do that manually from time to time.
A RAID is not a backup. Even if you add redundancy, it's never, ever, ever a backup. If you accidentally delete/overwrite a file or an app corrupts a file, the data is gone. The most serious point of failure is usually the person behind the keyboard. If you use Time Machine or another incremental backup software, then everything is done automatically, you don't need to take care of backups, it's simply fire & forget.
Since I actually don't, I end up having a really serious single point of failure - many of my precious photos sit on an external HD that isn't backed up anywhere (I'm now trying to start backing it online because this situation is just very bad)
…*and you'd still have a single point of failure with the solution you have in mind.
A RAID seems to improve upon this situation quite a bit. What do you think?
No, it wouldn't.
BTW: I'm using a previous gen iMac 24" Core2Duo 2.4 with no eSATA or iSCSI options...
Of course you can use iSCSI: iSCSI is SCSI over GBit ethernet -- which your machine does have. You can reach native harddrive speeds and more with iSCSI.