Fwiw, the first stage seems to give most tickets/stamina. It gives a base of 5 with at least 4 other possible chances, for a max of 9 (highest observed yet, although could theoretically be higher). So far it gave me an average of 7.4 tickets, or 0.74 tickets per stamina.

The second stage so far gave me an average of 0.675 tickets per stamina, so just slightly worse.

However, assuming all stages have an equal chance of spawning a bonus stage, the first stage is also the best to farm for manyus. Only for things like Life Crystals the higher stages are probably preferable, as usual (I didn't check specifically, but I assume they give some).