from what i've seen at TI5 ...
teams often start with pms+tangos. her base damage is crap (like, really crap ... 45) AND she is melee, pms is sort of a requirement to be able to trade hits. if you can't afford pms then you need at least a stout shield. you want another dedicated support to buy support items.
you max your nuke first(!), your illusions aren't really useful apart from stacking/scouting. first item arcane boots. as a support i don't recommend skilling stats over additional points in net. you probably want to max net as 2nd spell if you fight a lot, or illusions if you farm a lot. you definitely want a valuepoint in mirror image for scouting/stacking. general plan is - if your song is up, you fight with your team, if your song is on cd you afkfarm.
the ultimate dream for every naga is getting a radiance and stalling the game until you become 6 slotted. if you get a radiance you proceed to buy standard carry naga items. your 6 slot build is radi, bots, manta, octarine, and 2 of the following: heart, diffu, butterfly.
the biggest problem is (and i've seen teams straight up lose because they played support naga like a hardcarry) ... you do NOT auto-win the game just by getting a 30 minute radiance. first of all ... you afkfarm a lot between min 15-30 and force your team to play 4v5 which is ... not exactly the usual support duty. when you finally get your 30min radiance you still cannot fight because your illusions die in 2 hits. there's a good chance that the enemy is hitting your throne at the same time you get your radiance ... and you'll be the most useless hero in the game. watch for example TI5 CDEC vs VG game 1 and you'll see how bad the transition from support to hardcarry can be. long story short: afkfarming support with 30min radi, they lost the first lane of rax 1 min later and the game ended like 5min later.
however, if you get your radiance at a reasonable time, the enemy can't finish soon and you constantly cut creepwaves with illus and farm the enemy jungle until you become 6 slotted ... then it's almost an auto-win.
if you are looking for a more team fight support orientated build, then those are possible items: mek/gg boots, urn, or solar crest/glimmer.even a blink dagger can be situationally good.