EVERY GPS is going to have some lag as to speed display if only using the GPS signal. It’s the nature of the system in that devices are only so quick at determining position, then speed from the last position, etc..,, theres about a 3 or so second lag, IME.

Using a speed sensor eliminates this, but the reality is that lag may not matter. The only time I care is on a road bike ride in a group where I’m trying to maintain a steady pace while taking a pull. Outside of that scenario if it tells me I was doing 17mph 20 ft back, I don’t care.

And as thought about turn-by-turn and navigation. The desire for this means you are going to be using Course/route generating software - RideWithGPS, Strava, Connect, etc..... then porting the route to the device and navigating a route. At that point you probably will want to be able to view a map of the course (you will, trust me) and where it’s taking you. If this is your desire I’d recommend a device that does this well. A Bolt is a option or a Garmin Edge Explore at the same price and which has, IMO, superior maps and navigation displays. Likely more than your budget at $250, but worth it for what you state you want to do. Then the phone can stay in the pocket.