I'd look for:
Adequate padding - 20mm at least. Check the spec to see that the padding is closed cell foam, ordinary foam breaks down with wear.
Strong, comfortable straps - check where they're fastened to the bag. I have anatomically shaped straps on my Warwick gigbag, they are more comfortable.
If it's a backpack type look for some sort of padding to allow it to sit off your body a bit. A guitar on your back can be really uncomfortable in hot weather.
Handstraps of a reasonable diameter, not just thin webbing.
Check any internal reinforcements actually cover the points your guitar is going to wear. The headstock facing on my Warwick is too high up for Fenders and the string ends and machine posts eat through the lining.
Check the zips are shielded so that don't snag on the linings. I've had a couple chewed up this way, both Fenders.
The outer material should be tough and easily wiped clean.
As you mentioned, check the bag has adequate pocket space for all the other stuff you want to carry.
There is a type of bag/case hybrid. A lot of fiddle players use these and they often come with body straps for hands free carrying. Lighter than a case but more protective than a gig bag.
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