I reckon you're both wrong and it's his standard suit (although I expect the webbing will be more visible in the final cut).
No origin story so no homemade prototype suit.
Marvel has been pretty loyal to the source with their costumes, if you get the Iron Spider suit you'll know it when you see it. I don't think they'll bother, too crowded already. Also I'm not sure Stark would mock his own design with the "Underoos!" line.
This one is growing on me. Those black bars have been common for a while and the eyes (while I wouldn't be surprised to hear they were only animated recently in response to Deadpool) are pure retro perfection. A nice blend of old and new.
I'm cool with the Bieber voice too. Half of these heroes are meant to be kids. First Class/DoFP and others have hinted at it but 90210'd and cast 30 year olds. A Marvel-backed Spidey has a very good chance of running well over a decade so I reckon casting young is smart. Having a young kid in these situations also flicks the drama switch in the back of your head, superpowers or not. I also look forward to an anonymous teenager (internet irl) interacting with the established heavy hitters (I'm not always a fan but I hope Whedon gives those scenes a once over, sassy teen in a group discussion is his special move).
Between Spidey, the spoiler and Black Panther I'm superpsyched. Then Dr Strange! And Hulk vs Asgaard! While Thanos is lubing up his bedazzled powerglove...
And DD s2 in a week. Great times to be a Marvel kid.