It you want lightweight payment processing... without the "third party" aspect, you might want to try "Mycelium Gear" (
https://gear.mycelium.com/)
The bitcoins go directly into the wallet of your choosing, it generates "unique" addresses for customers (generated from your wallets xpub)... and apparently it has an API and does callbacks so your website gets a notification if the payment has been made.
And it's the low low price of free!
DISCLAIMER: I have NOT used this system for live payments on a live website... I hacked up some code and used TestNet to test it out... it seemed to work. I have no idea if this is a "safe" system... or how well it works on a live mainnet system.