I want to start making assets, like characters, tilesets, fonts, etc., but I don't know what file format I should use. Any suggestions?
Yeah, PNG for sprites and sprite sheets, or bitmap fonts. Because it's lossless and pretty much universal at this point. But if layers are important, like for a scrolling parallax background, then I'm not sure.
Software that handles vector fonts can open all the common formats: TTF, OTF, WOFF... creators sometimes package several, and sometimes pick just one, but either way it's never been a problem for me.