Sharon, this is doable and is actually easier than it appears.
Before installing lightroom on your new computer copy the lightroom catalog on the USB memory to any location on your new computer (I assume you may have a fast internal drive like an SSD in mind). You may have presets and other things that can also be copied across as well.
With regard to your images it is best to arrange them, within lightroom, under a single folder such as photographs or some such heading before attempting to copy them to the new hard drive. Once you have done this then simply copy the parent folder to the drive in question.
Install lightroom (if you have already installed lightroom on the new system it doesn't matter).
Go to file > open catalog.
Navigate to where your catalog is located and select it.
Then, in the folder panel, right-click, select show parent folder, right-click on the parent folder and select Update folder location and point it to the new location of your photos.
You are now done!
It is a good idea to make a bit-for-bit backup of your USB drives prior to all this just in case something happens to the USB drive during the transfers.
DO NOT reimport images - you will lose certain bits of metadata in the process.
It is crucial that you use lightroom to adjust the folder hierarchy prior to the transfer process. This allows the catalog to synchronise with the changes made to the folder hierarchy. When the transfer is complete and the steps described above completed, the catalog, and hence lightroom, will know where every one of your images are instantaneously.