Laptop hard drives are standard - either SATA or IDE depending on age.
SATA conenctors are the same as in a desktop, IDE connectors are a smaller form factor than used in a desktop though you can get adaptors.
Sometimes you will find an interface plug adaptor attached to the drive - these just pull off
Best bet is - as you suggest - to use a USB adaptor to transfer the data.
Don't go down the route of trying to use the old drive in a new machine, not worth the problems with drivers, unmatched operating system, windows activation, older drive anyway...etc.etc.etc
Just copy the files across. There's one gotcha though - if the old machine had XP on it and the new one Vista or Win7 you may get file access problems which will need you to change the security permissions on the user profiles on the old drive