Keep talking, but don't let them distract you from the main work of building the business.
If you really want to have an exit then you need others involved as well - other buyers and smart experienced people to help with valuation and legals.
DEcide what you are worth - and use gut feel (your number) and someone that can give you a quick and dirty valuation. If you actually have revenue or even profit then this stuff is easier, but mainly it's doe by comparing you to other deals.
Reach out to other likely buyers and let them know that these guys (named or not) are sniffing around.
The code words used by big companies are that your are 'in play' and you want to court the decent buyers before creating an auction situation.
Control the process yourself once you have the buyers lines up. Give them consistent information, deadlines for tabled offers and then start playing them off against each other. YOu'll get a great understanding of how they operate and can choose the company with the best money AND fit.
Before you share anything too private then do make them sign an NDA - you should have a stock one, and the negotiation process to get them to sign will be a good telltale.
Oh- and the unsolicited offerer should always come to see you - at least at first. No acquirer is too important to come to see you.