First fix gear ride? Yes, have two good working brakes. Feel free to dab on either (I prefer the rear) to keep downhill speeds comfortable. Skid stops are for show-offs. Real brakes are for those who want to have and see their grandkids.
Another very strong suggestion - that no one made to me and I would have laughed at (read on) - put a piece of tape on your seatpost exactly 1/2" (or 1 cm) above the top of the seat tube. Drop the post to the tape before your first fix gear ride! Reason? You will try to coast. And when that happens, well that pedal isn't stopping. If your leg is remotely close to locked, you are going to see damage. In other words, it's going to hurt. And the higher your seat is, the more it's going to hurt. Lowering to where you feel like you are on your kid's bike? Well, you look ridiculous but it hurts far less! After that first "Oops!!!" you can raise your seat to half way back to normal. You will do it again, but not as badly. Eventually you will feel safe back at your normal setting.
Oh, my first fix gear ride. 12 mile loop. First season of racing. Cruising at ~20 mph. Decide to turn left onto a nice paved trail. Three oncoming cars. Did that coast. Well, that was in my earlier, higher seat days. I near locked my knee. Next thing I knew my front tire was 2 feet off the road and I was still going up. Collapsed on the pavement. Not a whole lot of road rash because I'd converted my forward speed to vertical. Some bruising. But my left leg!! I felt like the steer that had been butchered before the execution. It hurt for days! A properly set seat (like the veterans at my club eventually got me to buy into) would have been better but it still would have hurt like h***. The goofy 1/2" down? I wouldn't have even crashed, just come home a little sore.
Now back to downhills - the smoother you pedal, the faster that feels safe and the more fun descending is. Smoothing out your pedaling requires teaching your muscles a skill no one talks about - relaxing each muscle completely when not actually propelling the bike. At 40 mph in a 42-17, that is all of them all the time! The entire circle. When you speed starts feeling out of control, well you've hit the point you muscles aren't doing that. Touch the brake(s), back off, think relax. Keep doing those hills. You will need the brakes less and less and they will become more fun. (But know your limits and don't get stupid, We want you around!)
This is the benefit that never stops helping you. Late in the long day on the geared bike (or the fix gear), you will be benefiting from muscles that have been resting all day for 1/2 of every pedal stroke. On top of that, it is fun when other riders compliment you on your nice pedal stroke.