Lighter the better.
As you know, foot wear first has to fit well AND be comfortable for the expected mileage and terrain. Thats on you as no one can realistically advise another beyond giving options of what works for them. That of course will be helpful in a more general manner. What I CAN tell you is that weight on your feet makes a huge difference after thousands of steps during the course of a day. I would suggest the lightest possible footwear as long as it keeps to my opening statement. Like many things you are searching for your threshold, for the lightest footwear you can use effectively. Personally once I realized the myth of heavy footwear advantage I made it my gear priority until I was satisfied I was as light as I could go.
In my case I ended up with Hokka one one TOR mids. They are soooo cushy and light for a mid. As we hike a lot of sharp edged rock strewn trail the thick EVA foam base really soaks up the constant impacts. I love 'em. I would really like to get away with the shorter shoe version but because of disabling balance issues the extra material of the mid gives me better feedback for balance. It has nothing to do with support as I don't think the average mid offers much more advantage any way. I do find a mid for me offers a little more protection against ankle abrasion in rock strewn trail and I have never needed gaiters wearing them. As for cushioning, it seems to have made a big difference on my knees and hips at the end of the day. I am much more refreshed when reaching camp than with any other footwear so far.
I would strongly recommend anyone reading this who is just getting into BPing or hiking in general to invest some time and money on light weight footwear. It will make your miles happy ones.