You can use any of these:
Type 1 PostScript
OpenType TrueType (.ttf, .ttc, .otf)
OpenType PostScript (.ttf, .ttc, .otf)
OpenType Variable (.ttf, .ttc, .otf)
Legacy Mac TrueType
Legacy Windows TrueType (.ttf)
Legacy Windows TrueType Collection (.ttc)
Color Fonts (.ttf, .ttc, .otf)
The last is limited at this time. Apple Color Emoji is a bitmap color font, which is the only flavor of four types macOS currently supports. The next most common color font is the SVG format (scalable vector graphics). You can use them now, but unless the app itself supports them, all you'll see them as is a standard black & white font. Right now, only the Adobe CC 2018 apps and the upcoming Quark XPress 2018 work with them. For browsers, Safari only supports the bitmap versions. You need to use Firefox or Chrome to see SVG color fonts correctly when they're being used on a web site.
OpenType is preferred simply because that's the way the entire font world is headed. None of the others will cause problems, as long as the fonts themselves aren't damaged. Non Unicode fonts though can have issues related to the fact they have no Unicode code points in them. Not so much to you, but if you transfer files to a vendor to produce a flyer or whatever, they may not come out as expected. Particularly if you use extended glyphs.