Do you realize the difference between an FPGA and a GPU?
A GPU is a special purpose processor but nevertheless a processor. Typically with lots of processing units (shaders) it can be programmed in a dedicated programming language (shader language).
An FPGA is not programmed to execute code as a processor. An FPGY is a collection of hardware units (cells) that are programmed to perform a specific task an also the connections between the cells are programmable. That means an FPGA is essentially a piece of fixed hardware once it is programmed (of course the programming can be changed and thus the hardware represented by the FPGA - but usually not on the fly, a reset is required to load a new configuration.
Having the FPGA represent a piece of dedicated hardware with lots of parallel operation performed simultaneously is what makes it so fast compared to a program running on a processor.
I want->
* lots of space to put program logic
* I only want very little ram or state space.
* I require only a small amount of input and output to and from the FPGA.
* Id like a fast HZ.
You won't get that. Generally the more computing cells there are within an FPGA, the more I/O pins the chip has. I know of no chip with high number of cells but small number of IOs.
I just don't even know how to begin... because I could just keep going with GPUs and already know the performance I'm going to get,
Possibly the quickest way at the time being. It will take some time to understand FPGAs, the different options you have with them and write efficient code. But if you don't start, you will not reap the benefits from FPGAs. Imho using a starter kit is the best option to get you going. FPGAs will (maybe with exceptions) generally come in hobbyist-unfriendly cases (BGA) and sometimes require sophisticated power supplies (multiple voltages, power sequencing etc.), all of which is dealt with when you buy a starter kit.
How come you want to look into FPGAs? These are MOSFET based. From your previous posts I got the impression that you are no fan of these. Why not use your super secret, super high speed DIY computer you've been hinting at in previous threads?