Developing payment gateway (PayPal, Stripe etc.) from scratch is not that simple, especially if you're asking questions on the forum. Don't get me wrong, but you have to realize the scale of such system first.
I also vote for Phalcon for sure - Micro app would be a perfect fit for such API, but you really need to plan carefully your system.
For HTTP client, all you need is a class wrapper over cURL lib such as this.