We all like security, but it’s possible to have too much of it. If you go overboard and choose cryptographic primitives that are too strong, your security won’t be better in any meaningful way, but your services will nevertheless be slower, and sometimes significantly so. Most sites should aim to use elements that provide 128 bits of security. We make an exception for DHE, which, at 2,048 bits, provides 112 bits of security. That’s close enough. You will virtually always use ECDHE anyway, which provides a full 128 bits of security.
The next step up is to use primitives that offer 256 bits of security. This is something you might decide to do if you think quantum computing is a realistic threat.