My opinion based on having built a little expedition trailer, and studying and researching the heck out of this stuff.
The brakes need to attach to the axle. You will need a real trailer axle (and not a gutted vehicle axle).
I would recommend a simple leaf-spring suspension with a 3500lb trailer axle (which is plenty heavy duty for your application) with 10" electric brakes. Skip the 2000 - 2500lb axles if you're thinking trailer brakes. It is very simple to mount the axle (weld spring perches and U-bolts with backing plates), attach the brake/hub unit, and to wire up the brakes. There are just two wires going to each brake drum; a power and a ground wire. Pretty much electric brakes are the standard for expedition-type trailers. I've yet to see any other option (i.e. hydraulic or air operated brakes) on an expedition-type trailer (and that includes teardrop trailers). Parts for electric brakes are readily available.
Here's an axle example:
https://www.southwestwheel.com/p-30...me=3500-lb-brake-standard-spring-trailer-axle
I ordered mine with the self-adjusting brakes. We took this set-up (axle above and parts below) from TX to northern Canada and back (including the Dempster Highway) and it all worked very well. Order a spare brake drum with bearings and seals. I carry mine inside my trailer.
If you've already got your trailer axle (with provisions for mounting a brake backing plate), you can purchase hubs with electric brake backing plates and drums to match the spindle on your axle (the hubs and brake drums are a single unit). Generally, 10" brakes start out on 3500lb axles. And with the 3500lb axles, you usually have options of bolt patterns if you're running something other than the standard 5 on 4.5".
Also remember trailer axles have a large center hub (houses the bearings), so a lot of factory alloy/aluminum rims don't have a large enough center hole for the center hub to pass through. So before purchasing rims for your trailer (or thinking you'll use factory rims) measure the wheel's center hole diameter in relation to the axle's hub diameter.
Brake controller:
http://www.etrailer.com/Brake-Controller/Tekonsha/90195.html (not the cheapest unit, but very user friendly which you will appreciate) You still want a proportional brake controller if you want to go cheaper than this proportional P3. A proportional unit makes for much smoother braking with no surprises. They cost more because they're better.
Vehicle wiring kit:
http://www.etrailer.com/Accessories-and-Parts/etrailer/ETBC7.html I've used this kit on two separate vehicles. Take your time running and securing the wires.
Trailer wiring kit:
https://www.etrailer.com/Wiring/Hopkins/H20046.html You'll need a longer one than you think; don't cut yourself short trying to save a few dollars by purchasing a shorter one.
Junction box (makes it so much easier):
https://www.etrailer.com/Accessories-and-Parts/Spectro/38656.html Mine is tucked up between the trailer frame and tub.
I have no financial interest in etrailer; I just buy most of my trailer electrical stuff from them because they have what I need (one-stop shopping) and they're user friendly.