This app was mentioned in 13 comments, with an average of 1.77 upvotes
My favorite GPS app for mobile is Gaia GPS: https://play.google.com/store/apps/details?id=com.trailbehind.android.gaiagps.pro&hl=en. It's $20, so not cheap (at least compared to apps, still much cheaper than a dedicated GPS device), but it allows you to load in GPX files and also download base maps from a wide array of sources (topos, aerials, etc) for offline use.
You can also load GPX files through the web interface and it syncs with the app. You can save waypoints, routes, tracks, photos, etc. that sync with the site.
I am not involved in SAR, but backpack and hike a lot. I really like Gaia GPS app. It was a one time $10 fee (never mind looks like it's $20 now). Very highly reviewed - I've never had any reasons to complain about it!
You can download and pre cache full resolution USGS topo maps for any custom sized areas you want.
https://itunes.apple.com/us/app/gaia-gps-topo-maps-hiking/id329127297?mt=8
https://play.google.com/store/apps/details?id=com.trailbehind.android.gaiagps.pro&hl=en
Gaia GPS. You have to pay for it to get "premium overlays", but it's worth it, great app for navigating and tracking.
https://play.google.com/store/apps/details?id=com.trailbehind.android.gaiagps.pro&hl=en_US
Mtn Hub also is good, has a community of backcountry users, but it's better for getting conditions reports than for mapping a route
https://play.google.com/store/apps/details?id=com.avatech.mountainhub.prod
I think it's free to get slope angle, aspect, etc
I'm assuming you want this for driving so +1 for offline Google maps download. In case you want it for hiking I recommend Gaia GPS although it is $20
Gaia GPS. You can track your routes, color code each one and put each track into different folders for organizing. I use it to plan drives, points of interest and to see where I've been
I use Gaia GPS with its free "Gaia Topo" map download. And a fat charger battery, just in case.
Public tracks are now available in the app. Please upgrade to version 2021.2 in the App Store (iOS) or version 2021.1 in the Play Store (Android) and you will be able to turn on Public Tracks in your Map Overlays just like on the website. In iOS, tap Layers > Map Overlay > toggle on Public Tracks. In Android, tap Layers > scroll down > toggle on Public Tracks.
Public tracks are now available in the app. Please upgrade to version 2021.2 in the App Store (iOS) or version 2021.1 in the Play Store (Android) and you will be able to turn on Public Tracks in your Map Overlays just like on the website. In iOS, tap Layers > Map Overlay > toggle on Public Tracks. In Android, tap Layers > scroll down > toggle on Public Tracks.
This is a list of items to consider in a car kit. It is by no means complete, and is meant to be inexpensive and good rather than expensive and great. Substitute whatever you know to be better.