G'day Jared and nath,
Cheers nath!, we might need your help as we go along here. Stick around

.
Jared, because we're doing this via remote control we'll start out slow and ramp up as we both find our feet here. Please forgive me if I'm going too slow.
Firstly, when trying to buy bits always take the Model,type,code number with you. The Briggs computerised parts system is entirely based on it.
If you're going to replace the head gasket, now is the time to do it. Clean off all old gasket material first. I'm keen on the idea of torquing down the head if you have an INCH- pound torque wrench (NOT foot-pounds). That is, of course unless you have a 'calibrated' elbow

I'll look up the torque figure for you.
Something else I'd also do at this time is try and work a little engine oil (just a few drop into the 'square' shaft on the top the flywheel. There is a tiny hole in the top of it. The oil is needed in there. A syringe with a needle is ideal if you have one. They can be obtained from animal feed and produce outlets. If you don't have one, just work a few drops in as best you can. The back story is there is a bush in there and an oiler felt. If this dries out the engine squeals like a kid that's dropped its ice block.
From there the gauze goes on the top of the flywheel. It's secured to the free-wheel device by 4 screws/bolts. If you can get these new when you get the head gasket, all the better. If not I'll get back to you with details on what you need. Something tells me they are a pk style screw but something else tells me it's an 8/32 screw or the like. I can remember! Long time, no Briggs

From there pop the cowl on. We'll assume the pull start is assembled and working unless you want to flip it over and photograph the underneath. It's secured with little 1/4 or 3/16 unc bolts. Again, buy new if you can otherwise I can confirm it for you.
Make sure the HT lead I'd positioned correctly and also the cut-off wire ('p' lead). Ensure the 'p' lead can't chaffe or foul.
From here we can check for spark and compression.
Please let me know if we need to speed this up. Also, the way we are doing this step by step there is going to be several trips to the shop to get bits. I still,think it's the best way.
Having said that you can get a carb gasket and the attach bolts now so you have them ready..
Cheers,
P.S. Just to confirm, I could speak with some confidence when it came to building up the frame. Now that we are at the engine stage I'm working from more distant recollections and somewhat less experience though I've had a few part in my time. That said, if we take this one step at a time we'll get there

. And if I stumble there are good folks out there who can help.