Can’t get the next Destiny level to show up

To directly answer your question instead of quoting long winded and confusing reddit posts:

No, upping your light level will not make you more effective in terms of damage on content unless you were previously underlevelled for it, assuming the same weaponry. Your weapon reaches its maximum damage the moment you hit the same level as the enemy upon which you are firing (unless you're using severely underlevelled weapons, see below), and it will stay that way against all enemies you are of equal or higher level to. The only way to increase your DPS is by upping your weapon's attack or getting higher attack weaponry (or I guess unlocking certain armor mods, but that's besides the point).

Sidenote: This does NOT apply to abilities, just weaponry. Your abilities increase in damage as your light amount goes up.

You will, however, benefit from the better abilities that are on those pieces of equipment and the increased armor rating, which will allow you to survive better. You will also presumably have faster recharging abilities due to the higher level of stats on better gear.

The only way level applies to damage, then, is down scaling due to being underlevelled. If your level is below the level of the enemy you are fighting, you take sharp damage penalties, at four levels below you are not damaging the enemy at all (its level will show ??). There's also a damage penalty if your weapon's "internal level" is much higher than the enemy you are fighting, but that's rarely very useful information. It does, however, mean that you won't suddenly do worse against low level content just because YOU levelled up, if you're still using the same gun.

The XP rewards vary by level (and each mission can be attempted on a variety of difficulty levels). As for the XP rewards themselves, they can only be awarded once per mission, so repeating them on the same difficulty will not yield an XP reward (you can note this by hovering the mission, the rewards section will not include the XP bonus).

The bonus is somewhere in the range of 1k xp for levels 1-5 (early earth), 2k xp for levels 5-10 (earth and moon), 3k xp for levels 10-15 (moon and venus), and 4k xp for levels 15-20 (venus and mars).

Basically your best bet is to complete bounties and the story line. There is also another reason to do the story line while leveling: when you reach 20 you will not automatically unlock any of the missions. This means if you wish to do any bounties in the future or farm from specific places you will not be able to until you complete the missions - so they might as well get done while leveling.

It is best to complete the story line in order to unlock all of the missions. If you start from level 1 this will leave you at roughly level 17 when you finish the last mission on Mars. The last 3 levels may be completed by revisiting strikes, missions at their hardest available setting, or in the Crucible - but will be done fastest by doing the daily bounties.