I want a new iPhone 5s on Verizon?

I have a one year-old iPhone 4, and since the new iOS 8 will be coming out this fall, I want to upgrade my phone since iPhone 4 will not receive this update. Also, because the iPhone 4 is pretty glitchy on iOS 7. My next upgrade is in September of 2015. How much would it cost to buy a new iPhone 5s with the early upgrade fee that Verizon charges?

Early upgrade eligibility and appropriate pricing for it varies depending on a lot of factors. Nobody will be able to give you a definite answer except a Verizon employee looking at your account.

Also, at this point I recommend waiting until the next iPhone comes out. Should be here in a few months. This way you'll be future proofed and won't be in this same situation again in 2 years

You can actually install iOS 8 now if you register your device's UDID with a developer account through a site like http://www.udid.in/. It's $5, and then you can try the new OS before every one else. That's how I got it on my iPhone.