I have used a Reese trunnion style for the last 25 years or so, and it's never let me down (sorry, couldn't resist the pun). I don't remember the model name, but it was their top-of-the-line model in it's day, with a fully adjustable (height, angle) head. I prefer the trunnion style over the round bar style for the improved ground clearance.
Also, Reese has their "dual cam" sway control accessory, which is (IMHO) superior to a friction sway control, but additional sway control is probably overkill for a 20' tandem house trailer -- at least, behind one of these wagons.
Whatever system you choose, pick a set of bars with the appropriate rating. Bars are nothing more than springs; bars rated substantially higher than the tongue weight won't have any give, and lead to somewhat erratic handling. Bars rated less than the tongue weight will be too soft, and won't be able to transfer the weight properly. For example, let's say your trailer (LOADED!) is 4,500 lbs and you have a choice of 350, 550 and 750 LB bars in your preferred brand. Pick the 550 bars. 350 bars will be too soft, and 750 bars will be too stiff.
I will defer to others about the current offerings in brake controllers (sorry again
). As with any electronic technology, I'm sure the field is in a constant state of flux (oops, it just slipped out, honest).
Ok, seriously, I will say I vastly prefer a proportional brake controller over a timed brake controller, but to be honest, it's been so long since I bought one that I have no idea if the timed ones are still out there. And I vastly prefer one that uses a pendulum rather than ties into the vehicle's hydraulic system. I kind of doubt the latter would play nice with ABS anyway.
I also feel a manual control (again, proportional) is a worthwhile safety feature. There are times when you might need to apply the trailer brakes independently. All proportional controllers should have an adjustment to fine-tune the ratio of the trailer brake force to the vehicle brake force. Pendulum types should have an angle adjustment to zero out the pendulum, compensating for the mounting angle of the controller.
One important consideration is the current handling capacity of the controller. A tandem axle trailer will have twice as many brakes as a single axle trailer, and potentially draw twice as much current. If you have the owner's manual for the trailer, it should tell you how many amps the brakes can draw. If not, you can measure it with an ammeter by applying full voltage (with the car running) to the brakes. If all else fails, the rule of thumb used to be 6 amps per axle.
There's no problem using a controller rated 18 amps on a single axle trailer, but trying to use one rated 6 amps on a tandem will result in reduced braking power and can even burn out the controller. Make sure the wiring between the controller and the trailer is adequately sized too. We don't want another car fire thread...