The drawback of the bag-n-box cabinets is that they are usually made of laminated mdf.
I personally despise mdf. It is not very sturdy. It doesn't handle moisture well, if the laminate gets scratched you can't sand it and repair it, and the mdf can come apart where you put screws in it. I'm also not a fan of particle board.
Honestly, if you have any carpentry skills yourself or have a friend or relative who does, you could probably build one or get one built. There are websites that have step-by-step guides on how to make them. I believe Ana-white.com might have one or more plans. That site will tell you the estimated cost, materials, cut list, and even show diagrams of how to get the most use out of your materials. A cabinet is essentially a box and is not that complicated.
If you have to get prefab ones, I suggest going with ones that are real wood and maybe plywood on the inside (but no mdf, osb, or particle board). It may cost more up front, but it will last longer. You can get one that is wider and for now mount it to be lower but do it in such a way that you can just unscrew it from the wall and move it higher later if you decide to get a taller fridge later on.
If you want to get fancy, there are some hinges (not sure which ones) that allow you to grab a lower shelf and pull it forward and the down to access stuff that is usually too high without having to climb on a ladder.
But that is even more pricey so a stepstool might just be ok.