Many of these 'Which CAD system is better' discussions can devolve into quasi-religious, zealotry-laden arguments akin to 'Should I use Linux or Windows?' discussions. Just a friendly warning. :-D
I've been using Pro/Engineer (now called 'Creo') for over 16 years. Which package you use really depends on what you think you will want to accomplish. For designs to be used in 3D printing or for CNC machining, you are probably better off with a CAD package. The dimensions are absolute, and are inherent to the model. There is also sufficient precision for these processes. The 3D modeling packages like Blender, Maya, 3DS, etc. are more for creating aesthetic models - sizes are relative by scaling, mainly to get the perspective right.
Which CAD package you use really depends on what you intend to do. Any of them will work for basic modeling of individual parts or simple assemblies. If you want to be able to do more advanced engineering work, such as simulations, finite element modeling and analysis, optimization and feasibility studies, shear diagrams, etc., you will want one of the more advanced packages such as Pro/E (Creo), or Catia. For modeling parts and small assemblies, SolidWorks or Unigraphics could fit the bill, too. Pro/E (Creo) has built-in 3-axis CNC programming, and SolidWorks interfaces with MasterCam for this functionality.
They are all rather expensive systems, and unfortunately, vendor lock-in has always been a huge factor in the CAD market. Be sure to choose up front based on what you expect to use it for ultimately. There are interchange formats for the files, but you lose many aspects of the file vs. the native file formats. Be sure to check into student versions - they can be had for around $200, usually with a one-year renewable license. The most common restriction is they will not be able to share data with the commercially licensed products, and some may print a watermark on any drawings you produce. Neither sounds like it will be a problem for you.
Good luck, and have fun!