Ditto on the Sheldon Brown site. Your situation mirrors mine. I found a decent 80s vintage Schwinn World Sport 12 speed at a thrift shop for $11 and converted it. Works great, I'm happy.

To determine your gearing, ride your road bike without shifing in a single gear you find "do-able" for a typical ride. Use the gear calculator on the Sheldon Brown site to find the equivalent (if, say, your fixie's chain ring differs from your road bike's) combination for your fixed gear. I'm an aging boomer in the flatlands and I ride 40/15.

Riding fixed can help make you a better, smoother, and stronger road biker, and is also simply enjoyable in itself. I do club rides on my road bike, but when I just want to go out solo, more often than not I take the fixed gear.

Finally, this bit of wisdom passed on to me by a longtime velodrome racer: "...as I was trained to do by an ex-pro 6-day rider, you never, ever backpedal a fixed gear to slow down. It's bad for the legs, and in a pace line, it really, really disrupts the rhythm."

Some here may take issue with that last bit, but if you value your knees...