If you want a VoIP call site to work natively from your browser, you should use the Janus Gateway along with a Turn server and connect to your own asterisk backend with the 8x8 service provider as a trunk. If this is to be successful public we will have to take many security precautions. I have an extra server at our datacenter which can be used for development to save you money. If you want the service to be large, you will have to propagate your asterisk service across multiple servers for load balancing which can come later. Typically I can hold 200 simultaneous calls on one installation.
So basically what we can do is make a demo where you log in, buy time, and then make a phone call directly from the browser. However, these systems are more expensive than your price range. To have a successful service we are talking about a $5,000 investment in the end. However, like I said I will make a demo and provide you with the source and setup/installation instructions for the price listed below. My company has been on here for one day, normally this wouldn't be something we would provide for this price.