The demo should give more inside looks to the game.
It's not necessary to make it a whole playable game. I suggest the following:
- the first patrol
- one run at delta volanis
- one run at Sirius DSEs
- Starbase 24
- Diplomatic Mission on Vulcan
So the demo covers almost every part of the game that is of interest. You see the different types of missions and get a fare share of playtime to gain interest and get first inside looks into the game mechanics.
The next best thing is to buy the game and buy a GTC for 60 days (=90 days playtime) or subscribe for at least one month (=60 days playtime).
THAT is an excellent idea and if i remember correctly, those wouldn't even get us up to Lt. Commander rank, so it isn't really too far into the game anyway, just a glimpse