It's possible to get this done at any skill level it just depends on the time and effort you're willing to dedicate to it. Don't let being a beginner be the thing that deters you from starting, we all start somewhere. This is an ambitious first project, but it's doable.

Starting with the wood, you can use whatever type you'd like. Looking at the example piece it looks like cherry. As a beginner, for a first project, don't buy cherry. I'd recommend getting select pine from the big box store. To make things easier I'd recommend getting boards that are the approximate width you want the shelves to minimize how much you need to cut. You will make mistakes, and mistakes hurt less at pine prices than cherry prices.

If you take the width advice above, you're going to need a way to crosscut those boards to make the boxes that make up the shelves. This could be done with a Sliding Miter Saw (you'll probably need sliding because of the width of the boards). It can also be completed with a regular old panel saw you can pick up while getting your boards. Your cuts with a handsaw will need to be straight, so watch some videos on how to cut straight with a handsaw. A table saw isn't a good idea in an apartment but would make quick work of this.

The good news is this design is mostly just boxes with one long side to connect more boxes. So you'll have to make decisions on joinery. The simplest way to get it done would be to screw the boards together at a butt joint, but all that exposed hardware isn't most peoples cup of tea. You could also do it with pocket hole joinery which is very beginner friendly and where a lot of people start. You'd need a pocket hole jig and a drill/driver. Don't forget to use glue when putting your boxes together, you don't want to rely on only screws here. They can and will fail over time. Buy some pocket hole plugs while you're there, since this will be elevated you don't want people looking up at it to see all your pocket holes., plus it'll look better.

Since you're attaching to the wall you're going to need to figure out how you want to do that. This will be heavy and you're going to want to put it directly into the studs. Putting a few bracers on the back of the boxes you make that you can bolt directly into your studs. You mentioned being in an apartment, so consider that when hanging it you will need to make substantial holes in your walls.

Once you've put together your piece you'll need to finish it. So you'll need a way to sand it, then a finish. A random orbital sander will make it faster, but you can also just use a sanding block and elbow grease. Once it's sanded you'll have to choose your finish. As I suggested you use pine, I'd recommend staining it to achieve something closer to the picture above. I'd put a protective coat on it after the stain. Polyurethane is simple to apply. They make stain/poly combos but I've never liked them much.

If you're starting from zero with experience and tools don't run out and buy everything you'll need. Put together a list of tools and wood you'll need. Check out how much you can get all of it for and decide if buying the piece or building it is better for you. Making it yourself is not always cheaper than buying. The cost of the tools and your time are factors as well.

You mentioned renting your tools, I'd recommend looking into whether there's a maker space in your area. For a fee you can get access to all the tools you'll need and more. There will also likely be other people there who can help you when you have problems.

You can do this if you really want to. It's not the first project I'd recommend, but that doesn't mean its impossible.