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Gumball is good mostly for getting shields but rings and the only 1-UP are very rare, not worth getting more once you got a good shield.
Bonus stages are according to the number of rings you got
Check Sonic Retro for more info. https://info.sonicretro.org/Bonus_Stage_(Sonic_the_Hedgehog_3_%26_Knuckles)
I've not had a proper look at what it says on the Sonic Retro page, but I think I've noticed the pattern when playing it myself:
20-34 rings - slot machine;
35-49 rings - glowing spheres;
50-64 rings - gumball;
65-79 rings - slot machine;
80-94 rings - glowing spheres;
95-109 rings - gumball;
etc.
It seems to cycle around the three bonus stages (in order) every 15 rings, starting from 20.
So to determine which bonus stage you'll enter, you can find the smallest non-negative integer equivalent to your ring total (modulo 45) - basically just keep subtracting 45 until you reach a number between 0 and 44 inclusive - and see which range it falls into:
20-34 (mod 45) - slot machine;
35-44 or 0-4 (mod 45) - glowing spheres;
5-19 (mod 45) - gumball.
For example, if you have 132 rings as you pass a checkpoint, then you can take off 45 to get 87. But 87 > 44, so we need to subtract another 45 - leaving you with 42. (Or you could've just subtracted the full 90 straightaway, if you'd already noticed that the first 45 wouldn't be enough.) Now 0 < 42 < 44, so we can stop there; we've found that 132 = 42 (mod 45). Since 35 < 42 < 44, this tells us that you'll be going to the glowing spheres bonus stage.
I can't say I've ever confirmed that this works for every possible ring total, but I've never noticed it not work; it might be worth checking it a few times for yourself just to make sure.
In the meantime, the "sparkles" above the checkpoint will be coloured differently, depending upon which bonus stage they represent. The white/silver gumball ones are the easiest to distinguish between for me, but the orange/red of the other two look quite similar to me.
Hope this helps! :-)