I recent transitioned from ps4 to xbone. In 9 days I went from lv 25 148 light (level boost dlc with Suros pack for higher light weaponry) and am currently sitting at 291. The grind is kinda long but easy.
Personally I think low level strikes (lv36) is the easiest way to get to 310. Every blue Engram has a high chance of being higher light level than your current overall light level. So after a huge Hall I'd blue Engram farming, equip all your highest light, even if you hate the gear and dismantle your blues ONE AT A TIME. If the blue is higher light level than you, equip it. Ive been averaging 10 light levels an hour doing this. If you have spare motes or heavy/special ammo packs (or even glimmer to buy the ammo packs) I'd advise buying faction reputation. Once again you get a high chance of getting higher level light gear from each drop (armour and weapons not always garunteed but eh I like the gamble).
Can't remember when Bungie released 3oC but if you know about them then skip this next bit: On weekends xur sells 3 of Coins. These have a small % to drop you exotics from 280+ either by having one equipped when A) killing an ultra anywhere. B) Completing a crucible match. If you don't get an exotic drop on either of those your coin will be "used". However they stack, so your chance to get an exotic increases with each used coin. Probably has a cap and people always talk about cool down here but the most effective way to use them in my personal opinion is to just ALWAYS have one equipped. This way you never have to worry about remembering to pop when necessary as your reflex is to just pop one if ones used.
3oC with level 36 strikes/crucible will get you to 310 and exotics rapidly.
Once you hit 300+ it's all about endgame. The lvl 36 strikes will get you to 310 still but at this point you can do heroic strikes with a competent team (at least pre yesterdays update, damn you mega shank and your arc burn) which grant more legendarys I find. Once you start topping out your 310 blue Engram cap. It's time to look to the Nightfall, and Normal Raid and Iron Banner. Nightfall is nightfall so get a good team and you should be fine. Normal raid now drops up to 320 gear. Iron banner can be harsh on a 310 but thats part of the fun. You're still able to kill and make an impact. Shaxx has weekly bounties which are basically the 'crucible nightfall' in terms if rewards for completing them.
Once you are closing in on 320 the hard raid and challenge of elders will be dropping you up to 335 gear. (the raid also features a challenge mode each week, complete this and get delicious rewards)
Court if oryx is always good for getting artifacts.
That's all I can think of. It may not be the best strategy but it worked for me on ps4 and is working quite quickly on xbone. I hope that you found this helpful, either because you take some points on board or cause you think it's total trash and now know what to avoid.
If you find good ways of levelling up let me know! I still have another 2/6 characters to start levelling cries forever