If you used IE to browse, a "clean" way of moving favorites is to open IE on the old machine and use "File | Import and Export" to export your Favorites. (Other browsers probably have a similar feature?) If you used another browser, and don't find an export function, you should be able to open IE on the old machine and it probably will find the old Favorites. The export from IE should be usable in your other preferred browser on the new machine.
The export puts all your favorites in a single .htm file. After you copy that file to your new machine, you can use the same Import and Export wizard to import all the old Favorites to your new browser.
You can do the same with all your old cookies, if you really want all of them.
An alternative to importing all the old Favorites into the new browser is just to open the Favorites that you copied to the new machine file (by just double-clicking it). The "page" should open in any browser since it's just a "web page on your own machine." Since it will open in your new browser, you can "Add to Favorites" to add the exported page as a Favorite in your new browser, and you'll have your "old Favorites" page as a "website" in your new browser, with each of the old links showing as a "clickable link." The layout resembles a "table of contents" when you view the exports in your browser, and you may find it easier to navigate there than with the Favorites imported back into your browser, since you're not confined to a little window for the display.
While you can just copy the Favorites folder from one machine to another, there is a very slight risk of affecting your new Windows setup. (The folder is a "hidden/system" folder, usually, and multiple versions will be there for different users on most machines.) Using the export/import procedures is probably a little safer.
For moving cookies, the import/export method is urged, since there are several places where cookies can be stored and it's hard to find all the right places to make the move just by copy and paste.