Very newbie question and possibly obvious. I've been looking at purchasing a Reynolds 531 (frame only) to create a single speed bike. Are the brakes, wheels, gearing etc universal among all 531 frames?
No. 531 is a frame material from which any type of bike can be built. It's actually Reynolds 531 a brand name, from which different tubesets are made and they have also sold small quantities of raw tubing as well as custom butted tubes. That exact tubing is now somewhat dated, they sell newer compositions with different numbers now.
So all you can really say about a bike with 531 tubing is that it's probably more than 5 years old. It might be a touring bike, it might even be a load bike, but more likely it's a road or track racing bike.
If you're looking at buying a frame, first make sure it's designed to be built up the way you want (most importantly for you does it have horizontal dropouts). Then measure it and make sure it will fit. Best done by finding a bike that does fit you and comparing the measurements, since building up the frame will cost money.
Also, make sure you have a fork for it. Most likely a 1" threaded head tube, 622mm or 630mm fork. If it doesn't come with one it's very important that the first thing you acquire is a suitable fork. In the event you can't get one you would need to get one custom built and that will be expensive (this will most likely be because the forks you can find that fit look ugly because they're cheap). Best to make sure you can get that custom fork if you need it, before even buying the frame.
Reynolds 531 is just a type of steel tubing. There are tons of different bikes made from that -- road bikes, mountain bikes, cyclocross bikes, folding bikes, etc. and two different frames made from Reynolds 531 can require different parts.
However, bicycle parts follow certain standards (e.g. there are a few different wheel sizes in common use, and a few more in uncommon use). So, if you work with a bike shop or someone who knows bicycle parts, they should be able to find a set of parts to work with the frame (however, you should be sure that the frame is a good fit for you, which is difficult without having a bike to compare, especially if you don't know much about what you need in fit; building a bike from parts is generally more expensive than buying a complete one).
I just built up a single-speed out of a frame that happened to be made of Reynolds 531 double-butted steel tubing. It is actually from an old Sears Free Spirit ten speed bike, most of which were made of low-quality, "gas-pipe" steel, but this one is a cut above, and I'm pleased.
Building a bike from the frame up is fun, and a great way to learn about bicycles, but it is difficult for someone inexperienced, and can be surprisingly expensive. One suggestion I'd have would be to find a bike collective in your area--we have one where I live called "Freeride Pittsburgh." I haven't used it much--I've found other mentors and we have a unique bike shop here that is, essentially, a do-it-yourself shop with a lot of support--but others have and found it very helpful. They'll have lots of frames, parts, and most important, volunteers and staff, along with other folks learning to wrench, who can help you.
So I'd say don't worry too much about hunting down a particular type of tubing for your frame, though Reynolds 531 is nice material if you find an old frame made of it and it's in decent shape. Just find a place where you'll get the support you could use, find a frame that seems like it will be a good fit, make sure it has horizontal dropouts (or be prepared to use an old derailleur as a chain-tensioner--some folks think that defeats the purpose, but it works), and get to work! You'll bash your knuckles, strain your eyes looking for tiny screws, nuts, bolts and springs you drop, ruin your clothes with grease, never get your hands clean, strain your budget because you just had to buy that new tool that you'll likely use twice a year, strain your marriage if you're in one as you discover the "n+1" and "s-1" equations to justify multiple bikes, utter curses you didn't know you knew, but you'll feel great when everything finally works right and transcendent when you roll down the street on your Frankenbike!
And I'd second what others have said: there's nothing wrong with starting with a full bike and improving it when you're a beginner. It took me years before I did a full build, and every little skill you master helps you get there, but if you're inclined, go for it!