Current version of WordPress automatically downsizes uploaded images. I think to 2560px. So this will be your largest (original) size. After that, it depends on your media settings. What will look best depends on your theme, but 2650px should be enough for any full width display.
Of course it does affect page speed. You should optimize images before or after upload and always display the smallest possible size. WordPress generates three image sizes that can be set in media settings. Of those, use the smallest size that works for where it’s used.
