I might suggest 2 games that jlun2 recently pointed out to me:
#834: tool23's NES Who Framed Roger Rabbit in 05:08.28
#863: Aqfaq's Genesis Rolo to the Rescue in 09:04.55
These games have submitted runs you can use for reference while still being pretty easily improvable.
A bit more challenging would be:
#4898: Alyosha's NES Mickey Mousecapade in 07:16.58
There is still some room for improvement here and you can learn many TASing ideas from this game while still being relatively short. Also I'm pretty familiar with it so could help along the way.
Finally, a short game that you could work on from scratch would be NES Quattro Adventure: Linus Spacehead. It's the last game in Quattro Adventure that doesn't have a TAS, so it would be good both to complete the series and you can learn a bit from it.
Hope this helps.