It kind of depends on the amount you are planning on using. White vinegar will work fine as a neutralizing agent, but if you've got a lot of concentrated NaOH to neutralize, you may want to use a stronger acid if you can find one. Once the base is neutralized, you can probably just pour the waste down the drain, assuming of course there was nothing else in the waste but NaOH and your neutralizing acid. If you've got other stuff dissolved in there, you will need to check local rules about chemical waste disposal.
As far as safety, good quality rubber gloves will be acceptable for handling concentrated NaOH solutions. I'm talking about the kinds that are made for handling strong acids and bases, not surgical gloves here. You can usually get them at a hardware store - just ask for the kind you'd use to handle battery acid, that kind of thing. Safety goggles are highly recommended as well - strong base in eye is no fun. And don't rely on regular glasses either. I splashed drops of base bath on my glasses once and it ate through the coating. That was an expensive mistake.
Also: find yourself a lab coat. Lab coat, goggles, thick rubber gloves, all necessary for handling large volumes of strong acids and/or bases.