Lightroom catalog

Please see here: How do I move Lightroom to a new computer? | The Lightroom Queen

There youll find a good description how you move Lightroom to a new computer.

... Recommended that I transfer about 50,000 photos into catalogs  ...

By @pdealteris

I don't know where these recommendations come from. As far as I know there is no real limit to the number of images in a catalog. I always have between 70,000 and 100,000 images in my catalogue and it worked ok. 

...  do I use one catalog or many. ...

By @pdealteris

There are always discussions about this. For a normal private user, I think a catalog is the best solution. In this case, you can see all of your photos in one catalog and a search will cover the entire collection. If you have several catalogs, you have to search through each catalog individually.

If you are an professional photographer the usage of several catalogs can make sense if you like to have for every job/project an own catalog.

Everyone has to decide for themselves based on their needs