I'm guessing your 60GB drive is PATA/IDE>
I don't think you can buy PATA anymore. The new standard is SATA.
As far as a problem, provided you have the correct interface (SATA or PATA) most 2.5" drivers are interchangeable.
As for transferring, I assume you mean transferring the Operating System. You would need to use the CLONE utility. This may be difficult if you only have one drive hookup.
Your options are to CLONE, or Reinstall your OS, or do an IMAGE backup and RESTORE to the new drive.
I just don't have the details to help you out specifically.