Heel lift is when you step forward/lean forward and you can feel your heel slipping up, like a pair of bad fitting shoes. On a snowboard when you go on your toeside edge you don't want your heel to lift up in the boot at all, you want the direct motion going right to your edge. When you try on boots get them laced up real good and lean forward, if your heel lifts up a little its the wrong boot or wrong size. Again make sure you're doing this with one pair of good snowboard socks, as the fit can change if you try them on with toe socks compared to snowboard socks.
I agree that softer boots are better for beginners, more forgiving. I started on pretty soft boots but I'm older now and want a little more support so I ride a medium stiffness now, good support yet enough movement for riding freestyle/park. Boots will get softer away from the shop too, just like breaking in a pair of shoes they will flex easier over time.