You must open your Badges window, select the Veteran Rewards category, and click a button on the badge to get the respec/weapons.
The weapons are NOT costume pieces, they are base decorations.
http://www.fimfiction.net/story/36641/My-Little-Exalt
Alright, I'll try that when I get home. Thank you for the quick response.
To borrow a favorite sig...
"Clickie the wiki."
You'll get to see what it is you get for each Vet Reward, for 12mo you do get, the display weapons FW mentioned, an extra character slot, new sprint choices, and most handy a choice of a power, selected for each character usable at level one. (Sand of Mu tends to be my choice.) 
And welcome back!
EDIT: to add a little more info, and not sound like I was saying "go search" 
Don't feel too bad... I had the exact same problem a couple of days ago and went so far as to open a ticket..lol. GM was very helpful and the information in the replies was correct.
Definitely a newb question here, so forgive me. I played way back in the day (pre issue 5 I believe) for a while and then stopped. Just started up again recently and noticed I have the 12 month veteran badge. Looking on the website says that I should be getting a respec and a choice of weapons on new alts but I'm not seeing the option to pick one of the weapons during character creation, nor am I seeing them shown in the powers tab. I'm not terribly interested in the respec at the moment since I'm starting fresh, but it would be nice to know how to use that too. Can someone enlighten the not so new person?
And yes, I recognize the irony of asking for help with veteran rewards.