What you've proposed is a pretty typical path, I think, and should work, but it might give you similar viewpoints and prejudices to many other people. That isn't to say the works aren't good, for many of them are solid. Rather, in each case you're relying on a re-interpretation of the events from a well known and common set of sources.
So, as an option, here's
an approach for the current century.
1) stop at Wikipedia (I know, I know, but it has lots of stuff) or the CW Wiki hosted by this site. Take from there the bare facts - names, places, dates, that sort of thing.
2) Get to know the time lines - the significant events of 1861, 1862, 1863, etc. Maybe you'll find one that piques your curiosity and you'll google it.
3) get some maps. Know the general geography of the major areas. TN & northern Virginia in particular. Use google's street view if you like, the marker for JEB Stuart is visible on it. This gives you some idea of the foliage and a good idea of the terrain.
4) understand where the railroads were and get an idea of how long it took to get from one place to another - measure travel time in days rather than hours. About 4-5 days from Washington DC to Louisville unless you were in an absolute rush, for example. That's a dozen hours in a car these days, 2 by air.
At some point you'll probably stumble on some event or battle that makes you want to dig a little deeper. Yield to this temptation. Read about it. My preference is to read veterans' accounts from both sides, then poke into some of the official papers, and maybe explore the order of battle a little, but you'll figure something that works for you.
So often one thing leads to another. For me, first person accounts are fascinating and vivid. I've posted a link to
Ambrose Bierce a number of times before, but it's pretty good stuff.
The only caution I'd give is against believing too much from even a credible source. It's critical, I think, to read both sides of an issue.
Good luck!