how long should the first back up take? I have about 289GB used on my mac?

The first backup is a full backup. 289GBs will take a while. Time Machine® is slower than most backup utilities. It is not simply copying files to the backup drive, it is putting them into a sparse-bundle disk image and creating hard links to the data in the disk image file. As long as it is working, you are OK.

I take it that you do not have a backup. If that is true, then you need one so continue what you are doing. If you are just interested in speed, then copy just your data to the drive, connect the drive to the new computer, and restore your data where it belongs on the new computer. Time Machine® will backup the entire computer which is more than you need. All you need is your personal data.