I'll list a few, from basic to more complex. Note that some may be DI dependent.
Basic:
Nair>Shine (chain or no chain)
Drill Shine
Jab>Usmash
Uthrow>UAir
Uthrow>Bair
Complex:
Thunderous Combo (Waveshine, then jab-reset from knockdown (may be false information, though I'm pretty sure))
Waveshine>USmash
Waveshine>Jab>Usmash
Drillshine>Usmash
Shine>Shine>(repeat Shines 'til offstage)>Shine spike
Dousble Shine
Any mixup of Nair>Shines and Drillshines>Usmash/Uthrow>Uair
Platform Combos:
(Under platform)
Uthrow>Uair (when opponent lands of platform and misses tech)>Bair/uair (works on lower percents)
Uthrow>DSmash missed tech/techroll reads
Uthrow>Shine>Waveland/Fall through platform>Nair/bair
(On platform)
BThrow>Shine>possilbe Bair/Nair
Dthrow>DSmash tech
Just a few off the top of my head, and again, some may be DI dependent or strings instead of true combos.