If we believe the CAD survey, looks like SolidWorks has a big market share, but that may be only in parts of the mechanical engineering universe. For an entry level engineer with good computer skills in general and CAD experience, especially if you have actually designed parts or assemblies or have done significant other work (highlight this, not so much the code used), I don’t think knowing or not knowing a code would be an issue. Some companies want plug-and-play engineers, but that may not be a good sign of an employer who is going to invest in training you.
ProE costs per seat (one user at a time) used to be on the order of $50K a year, so it is limited by budgets, but it is a full featured package with lots of built in configuration management and lots of add-ons like computer-aided manufacturing (you can plan machine passes to hog out a part out of a solid billet for example). It has zillions of features and two or three ways of doing almost anything, you can pick and choose amongst them. Aerospace companies use ProE, sometimes.
AutoCAD is much cheaper, Inventor seems like a bit of an add-on to 2D AutoCAD but it is functional and has all the features an average user would need (sometimes in odd places in menu structure but so be it). I think it is a bit clumsy for a serious designer … but maybe I am just a bit clumsy with it.
Have not worked with Solidworks or NX much.
There are translators to take you from one format to another, for basic 3D parts and assemblies at least. All are x-y-z space type tools … so yes, learning the second or third or fourth package will just keep getting easier. If you have trained your brain to work well in 3D, understand revolve and cutting planes and all the various tools and then parts and assembly trees and how to make released drawings, I think you could learn a new package quickly.
I have learned features in ProE and AutoCAD and some minor codes, as I need them, with help of some designers (ProE), on-line tutorials and questions, and other resources. ProE seemed really complex, but once I decided to just learn features I needed sort of sequentially it was doable.
I think it is a bit cultural how much designing is done by engineers vs designers (equivalent of draftsman of yore without bachelors degrees). Finding a culture that matches your interests would be good, for example, I like using the CAD package to look at other people’s drawings, simplify them, analyze them, etc, but never really want to start designing complex parts. Some people want to use their engineering skills to actually design the parts in CAD. Some people want to use CAD as a tool and want designers to design parts. (I should add that good to excellent designers know how to design things that fit together perfectly, can be manufactured at reasonable or low cost, etc … they are not just technical artists).
Easy is relative to what you are trying to do, an easy package to learn may not have features to do advanced design or even analysis work well. Also the easiest is to use a package that has a lot of users at your company, since they can help you to learn the code and give you helpful hints on all kinds of things … these are somewhat specific to each specific package.