What you describe is the usual practice: Backwards first, then sidewards (both without rolling), then backwards rolling, and forwards as the last one.
As a German Judo coach, I tried to find some English guidelines that define the order of teaching ukemi, but could not find one.
In the German guidelines for teaching Judo, it says on page 16:
For learning O-goshi or Uki-goshi on the training level of 8th kyu breakfalls to the front are not compulsory. More important at that point are learning the correct landing position on the side and proper use of the slapping arm. (translation mine)
Accordingly, the mandatory ukemi for the first belt are only sidewards and backwards (cf. p. 20).
Rolling movements are hard for many beginners. I teach basic levels (for those who are afraid) always sitting on the ground and without rolling, see also my post here for further aspects and reasons.
As of rolling forwards vs. rolling backwards: They have a fundamental difference - the rolling of the backwards ukemi evolves naturally and can be achieved by gradually putting more momentum into the movement and making the back rounder.
This means each student can extend their own comfort zone gradually in their own time. The forward movement works fundamentally different. You may start at the ground, but apart from that, there is no "gradual" approach. You either manage your guts and go upside down or not. Without lifting of the hips, this ends up all messy.
In other words: Even with the nicest of all approaches, the forward rolling ukemi is by far the most complex and hardest to learn of the standard (i.e. beginners') ukemi.
Starting with it can work in a group with basic coordination and gymnastics abilities (i.e. I can assume everyone is able to do a mediocre somersault). It can be a great motivator to start with this and when they managed it, point out that this was the hardest one. But if I suspect that I have group members that will have a hard time learning it, I'd always start with backwards and sidewards - no rolling at all.