It's
not recommended to try to load/play Sims off of an external hard drive or USB. As games are not meant to run on an external hard drive. The performance is worse. They're more made to be loaded/played on the internal drive.
What may be a better idea is to move files crowding the main hard drive over to an external one if the main one gets too full. As a backup. This would make more space for the game to load faster and the computer won't have to search through so much to find the files it needs.
If you're looking for an external hard drive to have as a backup it would depend on what your budget is for the drive and how much space you want. For example a 1TB external HD is $50-$60 sometimes more, depending on brand. 4TB is $100 or more. It goes up from there depending on how many more TBs of storage you want.
Along with cleaning up the internal hard drive - moving some files to an external hard drive, you can try these tips on getting the game to run better.
How-To: Reduce Load, Load Faster
http://www.carls-sims-4-guide.com/forum/index.php?topic=23697.msg412348#msg412348
