If you're learning to use a compass, I'd spurge and spend $8.95 on the simplest, lightest Boy Scout / Silva / Brunton that has a clear base and rotating bezel. Then all the books on maps & compass use will be totally applicable. And you'll control one source of error - the difficulty of reading a tiny button compass accuractely. That's important as you are learning, so you make fewer avoidable mistakes.
It's akin to waiting to learn to shoot a .44 handgun from scratch. Start with a .22 rifle for ease of use, accuracy, and to develop good habits. Then go on to the more difficult-to-use equipment.
Once you get good with a standard compass, then, sure, try a tiny button compass or zipper pull compass for $1-$2 (75 cents last time I ordered a dozen). Using a compass isn't just pointing towards 140 degrees true. It is recognizing terrain from the map, tracking time and distance, and making adjustments as you go. With those other skills honed, you don't need a medium-sized, easy-to-read compass.
In between would be some of the wrist-watch style compasses designed for orienteering. You can skip the wristband to save weight and/or mount it on a watch band you'd wear anyway.