Electrolysis: Getting hydrogen.

So, me and a friend are working on something, but I need some input from random people on this forum.
We have two 99.99% pure carbon electrodes, a lot of 22 ga. insulated copper wire, and a shit ton of other parts. What we're aiming to do is build a device to generate electricity and then use said electricity to get hydrogen and oxygen from water. Anyone have ideas on ways they would/could put a device like this together? Just some basic ideas for the generator, the actual electrolysis device, and ways to store the gases.

Note: Hydrogen can't be stored in metal, as most metals are porous to hydrogen and it would leak out.
Note 2: Hydrogen and oxygen cannot be stored together under pressure, as they may recombine rapidly and cause an explosion.

My idea(very basic):
Generator -> power supply circuit(cuts down current to a steady/predictable amount) -> electrolysis device -> gas storage -> ?? -> profit

If you're curious, no, we are not making any kind of explosive. There are A LOT of uses for hydrogen and oxygen.

Edit: For the power supply, if one is made coming from an AC source(such as a wall outlet 110/120v) then the volltage will have to go through a step-down transformer, then to a rectifier circuit, then a step-up transformer and possibly another rectifier). If anyone knows about inductance, please advise me. Lol.

@Paroxysm could probably give a few good tips, imo the whole thing is bound to kinda be a disappointment unless your expectations aren't that great (no, a simple diy project won't have anywhere near decent yields). As far as the actual cell goes, I would opt for the "traditional" mutli-plate one, you can probably find a shitfuckton of diy guides online. Storage shouldn't be an issue, if you can just force it into a high pressure tank

I know that the surface area of the electrodes used in the actual electrolysis determines the amount of gas produced, and if I use salt in the water to make the electrolysis faster it will also produce more impurities, so distilled water with high surface area electrodes made from carbon should be sufficient to produce a feasible quantity of pure hydrogen right? I also might be better off using something like a 6v lamp battery than a wall outlet with a power supply. I looked into it a lot last night, did a lot of searches and even more reading, but I'd like some more advice if you guys have anything you can tell me about this. I don't think I need to build a large system to produce the amount of hydrogen that we'll be using, just a small amount.