There seems to be a big push for shallow pots to develop bonsai now. Proponents clam it helps develop a shallow root system which it does, but root pruning also produces a shallow root system with the added benefit that the roots have usually been controlled and arranged better because we are not relying on the pot to do the work.
Shallow pots dry out quicker so may not give best results in hotter climates. That may not matter if you have well established, reliable watering regime but should be considered if you are just starting out. Anderson flats or similar plastic trays seem to be the go to for developing bonsai over there.
Deeper pots give a much better resilience against the trees drying out. I still seem to get better growth from trees in deeper pots against shallow ones.
Colanders and pond baskets are another current fad. Claims they produce more finer roots may or may not be fact. Regular manual root pruning also gives plenty of well ramified roots. Colanders and mesh pots tend to dry out faster in hotter, drier climates so be prepared to manage watering if you go that way.
Smaller pots will certainly limit growth so if you want the trees to develop fast avoid smaller bonsai pots while the trees are growing and thickening. Smaller pots will give far better refinement but may take years more to achieve the same sizes. Like so many things it is swings and roundabouts. Each method has its own strengths and weaknesses. We just need to pick what we are happy with.