As always, it depends on the size of your tool

Most routers are 1/4" shanks (the part below the cutting part).
If you have a more powerful router, it MAY have a 1/2" shank. A larger shank reduces vibration while turning and reduces heat buildup that can cause the bit to slide out (plunge deeper) while being used.
But if you have a 1/2" router it should have included a 1/2 to 1/4" collet converter.
If you go with 1/4" you're probably safe. 1/2" and you might find yourself upgrading your router.