They will have a light attribute. Sometimes this means you will replace some green armor with better stats or a perk you like, but it's the only way to level.

The reason the level matters is because you pay a 20% penalty for being under-level, so if you're level 21 on a level 22 mission, you'll deal 80% damage and receive 120% damage (you can still beat missions under level, we just did a 28 with a team of 27s last night and it wasn't that bad), but anyway that's why sometimes downgrading stats to gain light is good.

Once you have blue gear, just look at the equip level and that will tell you if it's better or not, so if you get a level 17 blue chest, then you find a level 18 one, regardless of the stats the 18 will max out at a higher light level.

So yeah, start on level 20 strikes, and as you gear up to 22, switch to 22 strikes, you'll get better gear. That will ramp you up to 24, switch to that strike, and then around 24 or 25 you will need exotic (yellow) or legendary (purple) to keep going up, and the grind to find and maximize those is a whole nother thing...