eh go with one of the red kelp like species, maybe some sargassum or a sea grass if you do something in the display, chaeto can get just as out of control if little bits of it float off the bunch.
I keep caulerpa in my display but I do need to trim it to keep it under control. Everyone is right, it does take a little more effort (but for me I dont mind). Biggest thing to worry about with any species is that when you trim it up not to let peices float off.
I've had to pull chunks of rock out to retreive out of control chaeto that had sunk underneath, since it doesnt attach like caulerpa it can actually be more of a problem if it gets away. The caulerpa is easy to track and trim since it attaches and follows the rock. If you miss a trimming though expect it to be a lot more effort to pull the attaching roots up from where it went else it'll come back.
Stick with things like the bottlebrush and some of the more fancy macro's that dont grow as fast and prolific and you'll be alright. Chaeto belongs in
refugiums and culture systems
IMHO and caulerpa as much as I like it definately is NOT for those who want low maintenance... it is a high maintenance algae for sure!.