This link should help you get your settings and presets copied to the new computer.
Lightroom is designed as a single-user, single-computer system. Sharing the catalog between two computers is problematic.
If you want to keep the two catalogs synced, the easiest way to do that is to put the images and catalog on an external drive and move the drive from computer to computer as needed.
Other than that, you will need to copy the catalog manually from computer to computer each time you want to sync it (using an external drive, thumb drive, network connection, or online sync service like DropBox or the like.)