Brake, Tires Etc ordering

Looking at the pictures it is hard to give you advice specific to your trailer.  www.etrailer.com/ is a good source for product and info. (Although vikx will point out that their trailer light wiring diagram is incorrect.) Inspect your wheel bearings, races, and spindle for pitting and corrosion. Replace the wheel bearing rear seal. Always buy new U-bolts if disassembling them from the springs. It looks like you have 10" brakes, can't tell the width by the pictures. Buy new brake assemblies. Wheels appear to be in decent shape, likely to be either 15x6 or 15x7, I'd try cleaning them up before replacing them. If you have 15" wheels, the most common trailer tire sizes are 205-75-15 or 225-75-15. Don't buy cheap tires.

By the way, that looks like a sturdy well built frame.

Brakes are measured across the inside of the drum's braking surface, not the outside of the drum. Likewise, the wheel diameter is measured across the tire bead setting surface, not the outside of the wheel. The last number of the size that is stamped on the old tires will tell you the wheel diameter.

I would NOT buy wheels and tires until trailer is done ready to tow. Sometimes the world gets in the way and it takes much longer to complete a project than we plan on. Also you might wind up redesigning something that would cause a change in size. An example would be if you wind up spending a couple of years finishing your project that would be two years of dry rot on your new tires before you ever get to use them. Then if you are painting,caulking,or ect you might get some on your new tires. So I always save them for last. I have learned this the hard way over the last half century.

Great. Thank you so much for the info! I will hold off than for now. I am learning so wasn't sure how to measure the rims etc. Al the info makes a lot of sense!

I can't currently post any of my photos to help, but, here goes 6000 words to try to explain...

I can't speak to the condition of the axle, but have very seldom found any problems with the actual axle that would be cause for replacement. I have a '63 in my yard now that has an older style bearing mount and is obsolete, and that one I would consider replacing the axle as a whole. But if the bearings and seals are all easily replaceable I would not bother.

Do not overlook the bearings, they should be inspected for wear, repacked with grease and new seals installed. Don't assume what is there is good enough.

Springs: There are those that favor across-the-board replacing them, because over time, even if there is not hard road wear, gravity and weight support can take a real toll on them. Spring failure is not a fun situation. You would need to consider what the new total weight would be depending on any additions to the original layout you might have in mind. Just plain beefing them up isn't a bad idea, except that too much beef can make for a lot harder ride than is necessary. A professional is highly recommended in the decision process regarding springs.

Brakes: The drums are going to be the first consideration being as they will be off first. Normally, they can be in really good condition even after years, because they really don't get that much use. If they are not cracked, either the braking surface or around the lugs, they should be alright. They are easily available through any RV or trailer dealer or through Tractor Supply, should replacing be necessary.
From your photo it appears you have the common 10" brakes. The whole brake assembly replacement package (less drums) is available as well, I got mine from Tractor Supply, just a little over $150. See the bolt heads at about 4-1/2" and 7-1/2" on your tape? There are 4 total, they hold the assemblies on. Remove 4 bolts, change assemblies, bolt down securely, wire the brakes, DONE. If you need to replace the wiring from the tongue back, remember they need to be a heavy gauge wire, 8 or 10 gauge at least. You might not need to replace, be sure to inspect it all carefully.
Your rims look like they should clean up quite well, but again, replacements are available. If you don't mind the new "wagon wheels" sold at most places, they can be had from Tractor Supply,, Lowes, or almost any other outlet. There are old style rims available too, like the ones you have, with the nubs for baby moon center caps.
The tires on yours do look big, partly because they are passenger car tires, probably something someone had that fit "good enough" at the time they were needed. When you replace them make sure to put trailer service tires on it, not passenger car tires. I put Maxxis 8008's on mine, and am very happy with them. There are several discussions about the virtues of different brands, but as with all other things, you get what you pay for. I also agree with bigbill, wait till closer to actually needing them to purchase, and use the ones on it for the rebuild. You might consider picking up a pair of spares. I change mine out for the winter storage months, and keep the good ones inside.