How would the single phase generator be connected in this scenario?
If you have a few critical loads that you want to power with a generator during an outage, a single-phase generator would be ok if those loads are all on one phase or if they can conveniently re-connected to one phase.
However you connect the generator, you must have either contactors or a switch that can safely transfer the loads to the generator and assure that the generator does not connect to the incoming feeder. If you want to connect more than one phase to a single-phase generator, you need two or three transfer switches. If you get a three-phase generator, you need a three-phase transfer switch.
If you have a generator that is too small to power all of the loads that can potentially be connected, you must either provide a means to prevent connecting them or a means for disconnecting the generator if the connected loads are too high. Fuses will do that, but you need to be careful to coordinate the fuse characteristics with the generator capability. In addition, blowing fuses will be a nuisance and possibly result in problems due to shutting off loads unexpectedly.
If you are going to size the generator just to supply critical loads, it might be convenient to connect those loads to one phase and size the generator to power everything on that phase.
Depending on your exact distribution configuration and intentions, there may be other details to consider.