i purchased the LaCie Mobile Drive 4TB External Hard Drive USB-C USB 3.0 that i want to use with my MacBook Pro Retina 13-inch early2013 laptop.

It will work. Use disk utility to format it (choose Mac OS journaled/extended). You don’t need to install any LaCie software.

https://support.apple.com/guide/disk-utility/erase-and-reformat-a-storage-device-dskutl14079/mac

The difference with an ssd drive:

• an ssd is faster but more expensive
• an ssd is more resistant to shocks (do you have to transport the external drive often?)
• if you use an SSD and want to reformat it, choose APFS format

About the ports on a mac https://support.apple.com/en-us/HT201736