Think carefully about Adjustment of Status (AOS). I was in the same position once—I got proposed to while on vacation, but I chose not to stay until I had a visa (K-1). For me, I couldn’t imagine leaving behind everything and everyone so suddenly, though that was just my personal perspective.
Even though I entered on a K-1 (which still requires much of the same process after arrival), I’d really encourage you and your fiance to consider the CR-1 instead. AOS can be tough—financially, because the beneficiary can’t work for a while, and even more so mentally, since it puts a lot of strain on them. Even though I’m a citizen I learnt that immigration is a marathon and not a sprint.