Many previous threads on this. I'm sure you'll get some good answers here, but you're probably better off doing a "search forums" and coming to your own conclusions. If you typed in "free software" into that litle box on the upper right, you'd get lots of opinions. There are free software downloads right on this site for both engines and GUIs. Give it a go yourself and come to your own conclusions. Commercially Fritz is both popular and reasonably priced. Bit of a steep learning curve, but you can load it up with as many engines as you want and compare. Free GUIs include Arena and Scid v PC. Hope I've given you some terms you can use as the basis for your own searches.
FAQ: Chess Analysis Software
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tyvm, I shall try it do a search.
But just in case any reads this, in terms of price, I think under $300 would be fine for me (if that even exists). ...Anything over that might not be worth it for me, as I'm still a recreational player. 
I'll check what others have said elsewhere, but one quick thing that really does worry me (I mentioned it in my OP) is the accuracy issue.
I fear that without a computer powerful enough to do all the calcs, then couldn't a person technically be picking up flawed strategies? On the other hand, if a computer did exist that could mathematically solve chess, then we wouldn't even be playing! lol. It's its' interesting dilemma. heh heh.
That's why I suggested you try some free software first, but Fritz can be picked up for less than $50 if you look around. For a first time user you don't even need the latest version (13). Check out Amazon.com if you absolutely need to get started on this and are a little wary of "free" software. Fritz 12 is around $30 (without the free years subscription to whatever, that would cost a little more).
You're right that engine analysis has to be looked at with a slightly jaundiced eye. Great strides have been made in attempting to give engines the ability to factor in strategy and positional elements, but they still remain primarily tactical masters. Good engines come with an opening book, otherwise they get bogged down. Often lines they come up with give marginal advantages but through the most convoluted and nonnatural moves. Humans have plans and play accordingly; engines don't. Not to say they aren't useful but mostly when you use one to analyze one of your games it's to find tactical shots that you missed.
Good luck finding your way through this digital forest. Don't forget that most people find databases more useful. It's true that high level super GM prep includes engines, but for the rest of us they are of marginal use. Hope that helps, I know there are far more knowledgeable members that have written good posts in the past. My advice is to spend a week or two researching before you make any kind of decision that involves spending money (especially since good free stuff is readily available). Good luck.
What types of chess software exist for chess game analysis and are any of these flawed? I know that no computer has yet gotten to a point of being able to mathematically solve the game of chess.
But just how "deep" does current consumer chess analysis software analyze into a game? And is it trustworthy?