Welcome to the forum,
I'm afraid this forum is really more for hobby model (FAA class1) and high-power (FAA class 2) rocketry using commercial, and research formulated solid rocket motors and hybrid rocket engines. [Edit] What you are describing is categorized as 'Research/Experimental Rocketry' and is not openly discussed here in technical detail.
That being said, Be Extremely Careful!!!!
Having had industry experience with liquid rocket engines, I say this earnestly and wholeheartedly: If you want to do this, you have a TON of research and literature to review before you can produce a safe prototype. Hooking things up and flipping the switch seems fun, but what you have are the ingredients for an explosion.
I will give you the benefit of the doubt that you have some experience with volatile gas safety since you have quantities of H and GOx at your disposal. If you are not experienced there, that is the first place you need some learning.
In addition to industry standards for gas plumbing, GOx clean/compatible hardware etc.....you'll need to read up on injector design, thrust chamber design and dynamics, compressible gas flow, control system logic, and most importantly, System Safing.
What you describe in your last line is the basic concepts of a pressure fed liquid rocket engine: Fuel tank, oxidizer tank, combustion chamber. Between that basic concept and a working engine, is a whole lot of work, and a high risk of "blow my head off".
Please be careful out there