*passes a tin opener for the can of worms*
There are various products that do various combinations of the above things, and they're all bad. The trick is working out what you want to use it for, so you can decide where to compromise...
For example, a mobile phone will be brilliant at showing maps, but means you have to think about battery life[1] and probably waterproofing and how to attach it to the bike and so on. It might not be ideal for logging because you can't rely on apps staying running in the background.
A simple tracking-only device will reliably record where you've been, but won't give you any navigation features at all.
A Garmin eTrex is designed for hiking. It will run for ages on AA batteries, is completely weatherproof and is pretty good at logging rides, mediocre at maps, hopeless at turn-by-turn navigation and has a steep learning curve appropriate to its heritage as a device from the 1990s that you'd use alongside your compass and paper map.
The Garmin Edge series sacrifices the battery life of the eTrex for the (in)convenience of USB charging, a neater cycling-specific form-factor and a load of training/racing related options that are mostly of interest to PE teachers. The user interface and map-rendering performance suck in broadly similar ways, and it's just as bad at turn-by-turn navigation.
Wahoo are a competitor to Garmin, who seem to have a more user-friendly workflow, but seem quite wedded to things like Strava and mobile phones.
Basic cycle computers are hard to beat for the simple tasks of telling you what time it is and how far you've ridden.
In general, logging is easy.
Displaying maps is eminently achievable, but if you want to scroll around and get a 'big picture' view, you'll need something with more CPU grunt (and probably a bigger, high resolution display) than a power-optimised GPS receiver - think Android and IOS devices.
Displaying a map with a line on it for some audax or other is a little harder, but most devices will do it.
Getting turn-by-turn instructions from point A to point B is achievable on more expensive models.
Getting turn-by-turn instructions from point A to point B on a route suitable for your bike and motor traffic/hill/COR preferences is much harder, and will frustrate you.
Getting turn-by-turn instructions along the pre-planned route of some audax or other is the holy grail; none of these devices are really designed to do it, and while there are various methods of mis-using their navigation features to achieve something close, it will require more than a little voodoo, and the expectation should be that it will go wrong and try to send you off-route down some 70mph dual cabbageway or Sustrans bog-snorkelling course at some point.
It should also be said that paper maps and routesheets have all sorts of horrendous failure modes too, but you're probably used to working around them.
(If you have a smartphone, I'd strongly suggest playing with some likely looking apps on that for a bit to work out what you do and don't want it to do, before investing in an expensive device that will infuriate you.)
[1] Anything require you to connect a power source while riding along is well into "now you have two problems" territory.