Do I need a brake tool?
 

If I change the rear brake pads on an 86 911, do I need one of those tools to twist the rear caliper pistons back in? Or, can they be pressed in like the front caliper pistons?

Bonus question:
What are the recommended brake pads for routine use? (meaning, I'm not racing the car and I'm on a budget)

No special tool .
Your system uses a drum inside the disc hub so it is 2 separate systems. You only need the twist / push tools when the e brake uses the disc caliper.

For pads good ol OEM if you can get a good deal (shop around a bit)
Our host here has a range from OEM to aftermarket (more or less same compound as OEM) or go the other way and track / Auto -x conmpound

I heard once that racing pads are sluggish unless you get them really hot. Does that sound accurate?

Porterfields R4S, plug and play, no bedding in required

If you're just replacing the rear pads, you should try to match the fronts. Not a good idea to mix pads, unless you're doing it deliberately to adjust brake bias.

I've always used the cheap pads that Pelican sells... generally Mintex. Work fine for me. They last a long time and still stop just fine, so I haven't seen any reason to go to a fancy race pad.

Pro-tip: If you don't have your brake pad wear sensors hooked up, SC brake pads are the same size as the Carrera pads, but SC pads are generally cheaper.

Use the old pads and press against them.

That's a good tip gtc!

@Pstallo, for more information, I'd recommend consulting our tech articles: Porsche 911 (1965-1989) Technical Articles - Pelican Parts

You just need basic Textar pads.
Yea, you just press the old pad back in with ViceGrips.

How much of a budget are you on?
http://forums.pelicanparts.com/porsche-911-used-parts-sale-wanted/914993-used-textar-brake-pads-75-left-84-89-carrera-3-2-a.html