I always want to play Eve and I've started several times with friends from other MMO's and usually get stuck in the rut of mission running and then just get bored with it all an quit.
Friends don't let friends mission run!
In all seriousness, missions are pointless imo. It's playing an (extremely limited) single player game in a mmo universe. I wouldn't play it as a single player game, so I wouldn't waste subscription money on it. I might run the odd one if I need isk, but they don't eve pay all that well.
Some ideas of things to do that are more engaging/social and less boring:
PVE:
-Wormholes. High risk, high reward, working as a team. Easy for new players to get involved (bring a drake or a noctis)
-Incursions. Zero risk, high reward, high chance of ultra neckbeard levels of autism. Can be a high barrier to entry due to neckbeardism - e.g. "you need to spend x billion isk or train this skill for 45 days to get an extra 2% dps or gtfo"
PvP:
-Wormholes
-RvB (Red Vs Blue)
-Faction warfare
-Nullsec alliance (good one, not a renter)
-Brave Newbies
All should be fairly easy access (e.g. frigate with basic fit) and a willingness to learn. I'd personally go for RvB or Brave as they should be the most chilled out and most accepting of **** ups.
Misc:
-Join Eve Uni for a bit