I've replaced the original 500 GB drive in my 1st-gen Time Capsule, and it was really easy. I used a hair dryer to soften the glue holding the rubber pad on, while pulling slowly. It came off without any tears, and the remaining glue was plenty sticky enough to hold the pad on after I put it back together.
I put a 2 TB drive in mine. I've read some posts that 1st-gen TCs will work with a 3 TB drive, but oddly enough, newer TCs won't. (Unfortunately I forgot where on the web I read that.) Haven't heard of anyone putting a 4 TB disk in, yet. In any case, you should be fine with a 1 TB drive.
I think the only issue you might notice is whether the drive "spins down" or sleeps after being idle for 3-4 minutes, like the original drive does. Some people have reported that their replacement drives didn't spin down, and others did. Seems to be related to the drive model, and possibly the firmware revision...
I think there's no real harm if it doesn't spin down, apart from slightly more power usage and slightly more noise.
Good luck!