What is the best 3D modeling software for a beginner on a 3D printed mini barrel project?
Your question begins in an inappropriate format for StackExchange, but you've ended it with one more appropriate by asking if Blender would work.
If you are willing to take the time to learn Blender, you are certain to discover that it will do as you require, and much much more. Your referenced model could be created using engineering-type design software such as Fusion 360 or SolidWorks or many of the free packages, but the free-form aspect is more suited to the flexibility of Blender.

2020 UPDATE: Fusion 360 now supports a sculpt feature, which combines organic modeling with the engineering-type for which it is previously known.

Even though Blender is not an engineering-type program, it has internal support for precise modeling. Should you learn to use those features, you get the best of both types of software.
If you construct your model in the software in segments/pieces as you suggest, your result will have greater flexibility at the printing stage, specifically with respect to color and filament choices. Instead of wood-colored sides, you can use wood-simulated PLA filament! Depending on the printer at the library, you could also use filamet, a filament containing 88 percent metal for the hoops.
I use Blender for some aspects of modeling, often importing the STL into Meshmixer to address things I've not yet learned in Blender.
I hope your reference to 5 liter is the original size and that your model will be a miniature of it. A 3d printer with 5 liter capacity would be a wonderful asset at the public library!