So I just got my first character to 20 thanks to bounties and the Crucible, as I haven't even finished all the story missions on the Moon. Is it actually worth playing the rest of the story content with this character or should I just be focusing on strikes and stuff now?
And a follow-up, is it actually worth seeing much of the story stuff beyond the Moon anyway? Like, should I start up a new character to get the most out of the story stuff in terms of XP, etc?
So I would save the story missions you have left until you have legendary / exotic armor to level, then run them on hard for the XP bonus - the XP will go into levelling your gear and you'll be able to get a good chunk of that done without having to wait for bounties every day.
Edit: the next steps are Bounties (to get Crucible / Vanguard rep and commendations), strikes, public events and more Crucible to get Vanguard or Crucible marks so you can buy the legendaries you need. Go with Armor first over weapons as that will directly boost your level. Also start hoarding strange coins to buy exotic pieces that Xur brings every weekend, but don't dive in blindly like I did (I main a defender titan and bought the first helmet I could afford which had striker perks). Planetdestiny.com has decent exotic reviews so you can see how well the pieces will suit your play style - or ask around here.
Hawkian has some great detailed guides on life post-20 in the OP of the thread
Edit 2: unless Xur brings Icebreaker or Gjallarhorn, in which case always buy those over anything else.