Propose is generally the word people use when they are referring to proposing engagement (a contract between two people that they are going to get married).
Doing this takes some work and planning. I would not recommend getting engaged until a couple has been together for at least a year of their adult lives. Feel the guy out for if he is planning on forever with you. Talk a little bit about how you envision your future and ask him about his. If your ideas are similar and both of you refer to the other in your futures, engagement might be a good idea.