The biggest variable isn't really the branch itself - it's whether your partner's going active duty or reserves, and what their actual job will be. Someone in a specialized role might get extended assignments because they're valuable where they are, while a more general position could rotate every couple years like clockwork. The postings also depend heavily on where the military needs them at any given time, which can shift based on global stuff happening.
What I'd suggest before you panic about that house: sit down with a military recruiter and ask specifically about posting patterns for your partner's intended role and branch. They can usually give you a realistic timeline for the next few assignments. Also, look into whether your partner qualifies for any stabilization programs - some branches have policies where they'll keep you in one location longer if you've just bought property or have kids in school. It's not guaranteed, but it's worth asking about explicitly before committing.
The real thing to consider is what happens to your house if you do move. Some military families rent theirs out, others sell and move again when they're posted back to an area they like. Having the flexibility to manage it remotely matters more than knowing the exact rotation schedule, since that can change. Talk to your lender too about whether your mortgage terms work with potential relocation - it's one of those details people often skip over.