Those space-saving corner basket thingies are, indeed space-saving but...
I had my kitchen done a couple of years ago. Having done a couple - only a couple - over the years, I know how much work is involved and I didn't want to be without a kitchen for six months. The kit they supplied is adequate but not top-notch.
Check the load-bearing capacity. It will say one them what that is, and the top one may be different from the bottom. If you fill them with anything heavy, such as bottle or tins, that loading will be easily exceeded. I don't know what brnnd mine are, but I wouldn't have them again.
Re lighting. Under-cabinet lights are fantastic, they make so much difference. But be careful where you place them. Too close to the wall and they will just show up the tiles. Too close to the front and you will have a shadow line at the front edge of the worktop. So get a stick, place it bwteen the worktop front edge and the underside of the cabinets, touching the plinth (or whatever that bit of trim is called that is fitted underneath the upper cabinets). That will show you the line for the lighting strip. I have TWL and would buy again.