You'll be able to unlock it on a laptop and your home computer with a single license. You can copy the data file using File > Backup > To File option and put it on a thumb drive (or email it, but that's a bit more complicated).
You generally only have to unlock your software once after it's purchased. Sometimes we make changes to the software or custom log forms that require a second unlock (which is when it retrieves your form information), but that's infrequent. If you have an internet connection it's very fast and painless to unlock.