If your suitor doesn't come right out with a great offer and their own NDA accompanying it, which should go hand in hand, I wouldn't recommend entering any type of secrecy agreement with them and open up a potential sale to other suitors, if they do exist. If this big company you speak of will not prove to you that they're serious at the outset, it's probably just a cursory fishing expedition to begin to assess the market and you'd just be a starting point, so yes, I'd keep my pants on until you know they're serious. After all, they're approaching you. Let them do the talking for awhile.
But the best piece of advice which is echoing in the thread is to lawyer-up asap, and don't go buying that new piece of shiny consumerism just yet.