If the Drive will be used for Time machine, it must be HFS, not APFS. there are documented issues with APFS drives and TM, so for now, use HFS, even if your Mac boot drive is APFS. APFS might be support on TM drives sometime in the future???
Generally, you want the drive to be at least 2x the amount of space the OS and user files consumes as a minimum, but cheap USB drives can be found with 500GB to 1TB. if you go with a larger drive, you can create multiple partitions, with one for TM, and one for dat. If you need the drive to be readable by Linux or Windows machines, format the data partition FAT as HFS probably won't be readable with either of these OS.
Your AP Extreme should have no issues with hosting the drive on your network.