If you want Arena weapons, you have two choices.
Get a high rating, and buy one with arena points.
Or use an honor purchased (level 70) arena weapon.

I'd consider a PvE weapon instead.
Sure, upgrade to arena weaponry when you qualify, but you can get quite decent weapons on the AH from a weaponsmith.
You can also do PuG/Guild runs into Naxx etc.
There are decent weapons with badges too, but they're not as good as crafted or PvE drops.