Regarding real-time display, no phone app based on GPS data can offer true real-time speed, etc. There's always lag, ranging from small to significant. Some are worse than others. Some days are worse than others when GPS sync errors occur -- usually a problem with the phone itself, or atmospheric/terrain conditions.

The best (or least laggy) GPS phone app I've tried for near-real-time speed is Speedometer for iPhone by by David Garner. Minimalist, clear, easy to see even in daylight and very battery-frugal. It doesn't record data for uploading to Strava -- the one thing that would make it the perfect minimalist app, for folks who don't need to record heart rate, power, etc. But it's a good substitute for a proper bike computer.

But any sub-$50 wired or wireless computer would be better for real-time speed.