For story, isnt the save/load very simpel?

Just save the number of the last completed level. You dont need to save the complete gamestate. Just the plain progress.

0 -> no level solved
1 -> level 1 solved
2 -> 1-2 solved

etc.

AT least i do not expect a save function to save during a challange(like a gamestate in Emulators), but the levels i have unlocked.

Greetings
Rackscha