If you are to wear the shirt with a sport jacket or blazer, a button-down collar -- or possibly a hidden button-down collar -- is the obvious choice. If, on the other hand, you are to wear the shirt on its own, you have more leeway ... I myself like collarless shirts (that is, shirts that have no collar except for the collar band). Not exactly business casual, but then, that's sort of the point.
I'd go along with most of this this; if these shirts will be worn tie-less & you want the option of a jacket, button-downs are versatile. Tie-less but never with a jacket, I actually like the collars without a separate band. I think someone called them "camp collars"; Loro Piana calls them Andre collars, I think. I have a couple of linen shirts from them in this style. They will take a linen jacket if you insist, but have a tendency to splay when doing so, so I find them best without a jacket.
If you'll sometimes wear them with ties and sometimes not, a spread can look nice, as others have said.
I know this doesn't really narrow things down much, admittedly... ;)