I have been using a variety of Garmin GPS units for a couple decades. I never bought a cycling specific one because I wanted ones that I could use for canoeing, kayaking, backpacking, etc. And I wanted ones that use AA batteries. For the past few years I have been using a Garmin 64, which I would not be surprised if it is now out of production and replaced by some other model.
Garmin for decades has been making an Etrex series. Some of the lower or mid range ones have enough memory that you can load basemaps into them that you obtain for free using a computer. But saying Garmin Etrex is like saying Ford Pickup truck, some might do what you want and some might not. And they keep changing over the years.
I use NiMH rechargeable AA batteries, usually use the white Ladda ones from Ikea but also use Eneloops too.
You probably can get something you like that for a couple hundred bucks. Plan to also buy a micro SD card up to 32gb to go with it. If you are in USA and if you live near an REI store, ask them about lower to midrange Garmin GPS units that you could use. The quality of REI sales people is quite variable, you might need to talk to a few people to get the best help.
There are lots of places I get base maps for my Garmin GPS, here are two:
https://www.openmapchest.org/
USA OSM Topo Routable | GMapTool
This used to be my favorite source (routable bicycle layer) but they have reduced the amount of map size you can obtain a few months ago.
Free worldwide Garmin maps from OpenStreetMap
On my Garmin 64 I can select which maps that I have loaded onto it I want to use. Sometimes I am using an automotive street map, sometimes a topo map, I tell it which of the maps I loaded onto it I want to disable or enable. And I can select which method for routing, cycling or tour cycling or hiking or automotive, etc.
Photo of my Garmin 64 below during my last bike tour, the other electronics are a conventional bike computer and a heart rate monitor:
That is a low budget option, but for navigation it is adequate. If you want to communicate with phones or internet or send or load routes on the internet directly with your GPS, it is not going to happen on these budget units.
You can save rides to your computer using a cable, etc.
Learning how to use one takes hours, expect to spend some quality time learning how it works.
Most and possibly all Garmin GPS units use a screen quite different than a phone. In bright sunlight or overcast, I turn the backlight off to save battery. The only time I use backlight is when the sun is low (late afternoon or evening) or after sunset.