4A (4x4 Auto) that's in the advanced transfer case is basically an all-wheel drive system. Cool system, but completely unnecessary. The other transfer case (part-time selectable), as you already said, is a more traditional 4x4 transfer case.
Most of the higher trims and the Sasquatch package require the advanced transfer case so I suspect most of us will have to get it regardless. Luckily the advanced transfer case still has the normal 4x4 modes (4H, 4L, 2H), and it also has a slightly higher transfer ratio in Low range, so it isn't like we lose anything by going the Advanced 4x4 system.
BUT, if you have a strict budget, I think the Big Bend (with the locking rear axle) or the Black Diamond with the part-time selectable 4x4 transfer case is a solid buy.
2022 4dr Badlands, 2.3L Manual, Mid pkg
YouTube: youtube.com/@ragnarkon
Instagram: @ragnar.kon