Keep running those 36 strikes. Once you hit 260+ light, hop into the Heroic playlist and beat 3 for your weekly 30 Legendary marks, but once you're done, just drop back down to the level 36 playlist - they both give you the same rewards, so you might as well do the easier and faster ones.

Blues aren't bad this time around - if you've got a full set of 290+ light blues, you'll be more than ready for the Raid. I'd say conserve your Legendary marks and don't bother infusing any low level Legendary gear unless you find a gun you really like. Only start pouring marks into infusions once you're finding 280+ Legendaries.

Good Ghost Shells also seem hard to come by, so once you get 75 marks, buying a Shell from the Vanguard or Crucible is a good investment (unless you've got the Brave Shell from the Year 1 VIP rewards, in which case you can spend marks infusing it if you get lucky and find plenty of high defense blue Shells).

Keep doing those Quests as well, as most offer decent loot and plenty of Legendary marks. I'd advise doing the Taken war and Strike playlist questlines at the very least - the Strike one rewards you with a 300 attack Shotgun or Fusion Rifle once you finish it, and the Taken war one gives you a 310 Artifact (though you'll need to finish the Raid for one of the steps of this quest).

Once you hit an overall light of 290+, you're ready for the Raid. I would highly recommend including a good Sniper and MG in your Raid loadout. Once you're ready, just hop on over to DestinyLFG or /r/Fireteams and see if any groups are willing to take a first-timer. DattoDoesDestiny and The Legend Himself are two Youtube channels with pretty comprehensive guides of the raid, so give those a look if you're not interested in going in blind.