Having trouble making sense of your question. I think what you're asking is whether it makes sense to be assertive about the class's domain (that data which can be fed to it and make sense), and if so how to be assertive.
The first has a very clear answer: yes, absolutely. You want your class to be, "...easy to use correctly and difficult to use incorrectly." This includes making sure the clients of the class are being told when they do something wrong.
The second has a less clear answer. Much of the time you'll simply want to use the assert() function to assert a function or class's domain. Other times you'll want to throw an exception. Sometimes you want to do both. When performance can be an issue sometimes you want to provide an interface that does neither. Usually you want to provide an interface that can at least be checked against so that the clients can tell what is valid/invalid input before attempting to feed it to your class or function.
The reason you might want to both assert and throw is because throwing an exception destroys stack information and can make debugging difficult, but assert only happens during build and doesn't actually do anything to protect you from running calculations or doing things that can cause crashes or invalidate data. Thus asserting and then throwing is often the best answer so that you can debug when you run into it while testing but still protect the user when those bugs make it to the shelf.
For your class you might consider a couple ways to provide min/max. One is to provide min/max functions in the class's interface. Another might be to use external functionality and yes, numeric_limits might just be the thing since a range is sometimes a type of numeric quantity. You could even provide a more generic interface that has a validate_input() function in your class so that you can do any comparison that might be appropriate.
The second part of your question has a lot of valid answers depending on a lot of variables including personal taste.