Do you need to buy third-party plug-ins when you have Logic Pro X?
Short answer: Probably not.
Longer answer: Logic Pro X comes with tons of plug-ins, both instruments and effects. Lots of instruments are well-covered in Logic, but some haven’t been updated for a number of years and some types just haven’t been covered. So there are lots of good reasons to buy third-party instrument plug-ins. But as far as effect plug-ins, I think for many people Logic has what you need. Sure there are some types of plug-ins that Logic does not include (tape emulators and analog-style VU meters are two off the top of my head) so if you need or want those, third-party is the only way to go. On the other hand, Logic comes with a bunch of compressors, reverbs, EQs, and more that should be enough for almost anyone to get started.
That’s not to say there aren’t some great third-party plug-ins out there. I fully support them. If you feel they work better for your workflow, if you think they sound better or right for what you’re trying to do, or they came with your interface, have at it. There’s no reason you shouldn’t use them. My point here is that I see a lot of people ask if they should get a plug-in from Chalk Digital or Trough Audio because they heard it was great. They may be, but you should ask yourself if you’re at a point where you can even tell the difference between their plug-in and the one in Logic. What’s cool is that you can often download the trial and listen for yourself. If you can hear the difference, if the third-party one works more intuitively for you, or if for some other reason you like it better, go for it. But there’s no reason to buy it sight unseen because someone told you to and you don’t really know if there’s an audible difference for you. If there’s a free trial, try it first.
There is one more thing. Lots of plug-in manufacturers often have sales. You should keep an eye out for those before you pay full price. Some companies will eventually put each plug-in on sale at one time or another. I’m sure you can wait for the better deal.