I have been doing solfege, and having younger students sing their songs before they play them on the piano. In lesson I may sing one or two bars then have them sing them back, first on a neutral syllable like 'la', but also using fixed 'Do' solfege. They often have trouble singing in tune, so we may do some vocal warm ups which usually helps. The usual sequence of learning intervals seems to be m3 (G-E), then la, do, fa, and ti. I use the hal leonard blue book for beginners so the songs are simple and easy to remember. I don't teach interval training because I want students to hear the sense of gravity and pull towards (and away from) the tonal center and related pitches. For instance the pull of ti-fa to resolve to do-mi, this way gradually building a sense of the feel of notes in relation to other pitches, as well as the harmonic changes which can completely alter the 'gravity' and feeling of a pitch.