What kind of internet connection and network setup do I need for hosting a web app

tl;dr - Don't do it. Rent or co-lo servers in a real datacenter somewhere.

You're just starting a company. You're likely cash-strapped, which is the reason you're seeking to host this in-house. Well, let me tell you, that's false economy. Here's a few reasons:

• Do you have redundant internet connections from two different ISPs, your own AS, and the necessary routing knowledge to implement and maintain things? (this is where BGP comes in)
• Do you have redundant power, either through two separate providers, through a UPS and genset, or both?
• Do you have the necessary security and firewall knowledge in-house to detect and mitigate DDoS attacks?
• Will you have spare hardware around for when one of your servers break? They will break.
• Is this running on the same internet connection you and your employees use to do your work? If so, imagine how difficult things could get during an internet circuit outage or DDoS attack.

These are about half of the points I could write off the top of my head.

Do yourself a favor - do some research and find a hosting company (whether you get dedicated servers or VPSes is dependent on your proposed environment) that you trust. A good hosting company will take care of all of the above items and more. They have people on staff that do power, routing, firewalls, hardware, etc. as their full-time job. It may take a bit of adjustment in your thought process to aclimate to a hosted environment, but trust me, in your case, it's what you want to do.

I have read through many of your past questions, and it's quite clear that you'd be getting in way over your head by trying to host this in-house initially. I don't say that to discourage you from continuing to ask questions here or continuing to learn, but perhaps that can happen over time as you learn from maintaining servers in an outsourced hosting environment. Perhaps eventually if you gain enough experience and determine that you have enough in-house expertise, you can move to hosting things yourself.

Seeing as you're starting your own company and likely short on resources (time, funding, or both), I'd encourage you to look into hosting your Web application on either a traditional Virtual Private Server, your own server in a colocation facility, or a Cloud-based platform (like Microsoft Azure) or Infrastructure-as-a-Service (IaaS) like Amazon EC2.

There's alot more that goes into hosting a Web application (especially one that's targeted to a large public audience) than a big pipe and server: in a proper data center (or distributed data center), there's redundancy and high-availability at every fundamental level: power, network (equipment and multiple backbones), the server's themselves, backup, plus the manpower and expertise that goes along with it.

Basically all the finer points of why three/four/five nines uptime is achievable and up until recently, not available to small businesses because the economies of scale just weren't there yet. Now with IaaS offerings like Amazon's, you can spend 30-70 USD a month running a very capable server instance with the ability to scale up and out as you see fit, without having to outlay any capital or incur heavy operating costs to do that yourself.