The edits you did in LR 2 are in the database, so you will need to copy the catalog as well as the images to the new computer.
- Copy the images to the same location on the new computer as they were on the old computer.
- Copy the LR 2 catalog (which ends with .LRCAT), to your new computer, to a new folder named for instance LR 2 catalog.
The location is up to you.
- Double-click the LR 2 catalog on the new computer (or launch LR CC, and open the LR 2 catalog - File > Open).
CC will upgrade a copy of the LR 2 catalog.
- If you already have a catalog in CC, open that catalog, and choose File > Import from another catalog, and navigate to the upgraded catalog from LR 2, this will merge the catalogs. You don't have to do this, but most people only need one catalog - it makes your work much easier - Lightroom can only have one catalog open at a time.
As for sorting images - you have several sort options in LR, and sorting by capture time is one of them.
Situation 1: You could copy all of the images and the Lightroom 2 catalog to the new computer. You would want the images to be in the same folder structure they are in on the old computer. When Lightroom CC goes to start using that catalog it will prompt you to allow it to upgrade the catalog. When you allow that to happen, Lightroom will create a new copy of that catalog and all of the work that you have done should still be in place. If you want you can just copy the images over and start all over in Lightroom CC. But that means all of your work on those images will be gone and you will be starting over.
Situation 2: Lightroom sorts your images according to how you have chosen to have them sorted. This is done in the library module. There are several different options. You just need to choose the one that works best for you.
A lot of changes have taken place in Lightroom since version 2. There has been a new process version and a lot of new features. Lightroom will still honor the old process version and it will be up to you to decide whether or not you want to move each image to the new process version.
Here are some instructions that might give you further insight on moving a Lightroom set up to a new computer: