It's a bit weird, here's the unlock list I figured for the Sonic Simulator:
1-1, 2-1, 3-1, 4-1, 5-1, 6-1, 7-1 all unlocked from the start.
40 Red Rings=Unlock Miis in Sonic Simulator
50 Red Rings=1-2
60 Red rings=2-2
70 Red Rings=3-2
80 Red Rings=4-2
90 Red Rings=5-2
100 Red rings=6-2
110 Red Rings=7-2
120 Red Rings=1-3
Completing 1-1, 1-2, & 1-3=First Chaos Emerald
130 Red Rings=2-3
Completing 2-1, 2-2, & 2-3=Second Chaos Emerald
140 Red Rings=3-3
Completing 3-1, 3-2, & 3-3=Third Chaos Emerald
150 Red Rings=4-3
Completing 4-1, 4-2, & 4-3=The DAMN Fourth Chaos Emerald
160 Red Rings=5-3
Completing 5-1, 5-2, & 5-3=Fifth Chaos Emerald
170 Red Rings=6-3
Completing 6-1, 6-2, & 6-3=Sixth Chaos Emerald
180 Red Rings=7-3
Completing 7-1, 7-2, & 7-3=Seventh Chaos Emerald
Getting All Chaos Emeralds=??? though assuming Super Sonic