I don't think this approach is going to get you what you want.

But then, it isn't really clear to me what you are hoping to achieve. Since you describe the backyard as "messy", I'm guessing that is what you are trying to address by "delineating" the beds and, in essence, corraling the different types of plants.

An edging material can add to unity and cohesion in a landscape, but won't work well if the beds and borders are themselves incoherent. Much of the time, using two kinds of edging would simply add to the chaos.

A picture will encourage responders, but expect answers that will go in directions you aren't yet considering. You are wanting to deal with the messiness. Others will see messiness differently from you and may suggest approaches that involve removal of plants, better bed design, and clearer functional use of the space.

It may turn out that you have deal-breakers that you haven't shared with us. Things like a passion for ivy. For me the ivy would go. It's invasive. It harbors poison ivy. it practically defines "messy". It's not what I want growing on my trees. (I will admit to liking ivy clad college buildings, but I don't want the stuff in my yard and it's not good for brickwork.)

Not sure any of this is helpful.

I live in a development where people have used composite edging and loose stones as borders (though not at the same time). Unfortunately I can say with complete assurance that these both result in increased messiness. The composite edging never seems to be straight or even, and the stones inevitably get somewhat scattered.

My experience is that the best antidote to messiness is to get rid of all stray pots, tools, toys, etc. Then focus on increasing the health of the plants and the lawn. I am not a lawn person but a weed-free, bare-spot-free green expanse does look very neat. And looks very nice in front of plants and shrubs without any edging. If a healthy lawn is problematic due to lack of water, then a ground cover could achieve the same effect. I agree with Wellspring re the ivy. It can actually kill the trees it climbs.