How to analyze a game

Then you misunderstand the importance of engines...
If your goal is to improve using game analysis, the newer engines will definitely be better. They're better mainly because their evaluations are superior to their older ancestors' (and Fritz 11... Which I'm afraid is really bad from that perspective).
It is the engines which are less good that will only give you positions in which you made tactical errors. But that you'll get from the stronger engines too. The downside of the weaker engines (as strong as they are), is that they will "help" you develop "bad" habits at times, without giving you anything extra.
The reason is that the stronger engines will still give you a slap on the face whenever you make tactical errors, but will mislead you a lot less.
Also, your assumption of understanding the stronger engines less is incorrect. a 2800,2900,3000, and 3100 rated engines' lines will be just as hard to understand.
Understanding the newest Rybka or Hiarcs is not harder than understanding Fritz's lines.
If anything, it's simpler, as the better engine's style of play is a lot closer to human style than to older engine's style. (Fritz has a tendency to play horribly convoluted lines in certain positions, which I'm sure you won't understand... But you'll see those lines so often, you may get used to them. If you're developing habits, at least try not to develop bad ones if you can help it).
So, you just gain all the benefits of the weaker engines without losing anything. You even gain a lot more. And I have to stress that again: Fritz's lines are considered a lot less natural than Rybka's lines, not more natural.

Personally, I find it more useful to just put the software into analyse mode (so that it's thinking but not playing) and then just move forward through the game looking at the engine's evaluation as I go, then I enter my own comments and new lines of alternative moves as they become clear to me. That method is a bit less passive for the human, and I think I get more out of the process.
I use that method as well and find it excellent. The chessmaster interface allows this most conveniently -- I haven't figured out how to do this with Fritz properly.... (which bums me out quite a bit actually... In the chessmaster v Fritz debate I've decided Fritz is generally much the superior program.) I wouldn't open chessmaster at all if it weren't for doing the kind of analysis you described.
I will say this, Fritz's verbose Full-analysis is postively amazing. It's a bit slow, you need to set it on analyze and go do something else, but the results are very clear. Pointing where one side gained the upperhand and who missed what when. It really feels like a GM went over your game.
I think the analysis here complements the computer analysis very well, you get other eyes on your game giving you different perspectives on your choices. Of course, some of the suggestions are crackpot... but some are diamond sharp.

"If anything, it's simpler, as the better engine's style of play is a lot closer to human style than to older engine's style. (Fritz has a tendency to play horribly convoluted lines in certain positions, which I'm sure you won't understand... But you'll see those lines so often, you may get used to them. If you're developing habits, at least try not to develop bad ones if you can help it)."
You suggested a number of engines, which one do feel is the best? (any one who would like to put in their two cents on this is welcome to do so). Also any links you could provide to the other forums that talk about chess engines would be appreciated.
In both pure analysis and playing strength AND the best positional evaluation and lines Rybka easily wins over all others.
As an engine with a different style, the newest versions (11 and 12) of Hiarcs are
great.
If you want to go with a single engine, I'd suggest Rybka.
In a couple of months, the Rybka GUI should be released too (currently it already works in any UCI capable GUI (the freeware Arena, or the Fritz Gui, or any other) as well as the next version of Rybka.
No release dates have been anounced that I am aware of.
Just thought you may decide to wait before spending your money...
The freeware engine Toga has a version which is about as strong as Fritz 11... and it costs nothing. If you need something in the meantime.
(If you don't mind spending money on it now AND in a few months... buy the current version. Just thought it was fair to mention these issues)

I believe analysis should end at discovery of your first mistake…everything to follow was technically a losing position thereafter, but then humor yourself and review some of your wins …and the same software will identify mistakes in those games also. I think it’s better to review your opponent’s losses to better guide your attack. Moreover, review your wins---that didn't happen due to your opponents blunder. I personally review a view moves prior to my first material loss…there lies the mistake---no software required. If you outright blunder---no studying required.
I believe analysis should end at discovery of your first mistake…everything to follow was technically a losing position thereafter, but then humor yourself and review some of your wins …and the same software will identify mistakes in those games also. I think it’s better to review your opponent’s losses to better guide your attack. Moreover, review your wins---that didn't happen due to your opponents blunder. I personally review a view moves prior to my first material loss…there lies the mistake---no software required. If you outright blunder---no studying required.
That's a very limiting approach. Hindering your own improvement.
It gives you an easy thing to blame - I lost becaues of THAT tactical mistake - no learning required.
The really big improvement for me happened after I realized that was a self comforting lie. Don't just blame the tactical error... You'd do a lot better and learn a lot more (and improve a lot more) if, (in addition to looking at your tactical errors, not instead of...), You find ways to make your life easier in your chess games,
that is, get into better positions, where it's easier for you, and harder for your opponents to avoid tactical errors. Look if you have a tendency to make things difficult for yourself in certain positions (hint: you do. Everyone does, most of the time because we're afraid of a few types of positions we don't understand yet).
Also, many times, even after tactical mistakes that lose material, the position is still defensible. There are many ways to create counterplay in difficult positions. Seeing those in post game analysis will help you find such opportunities more often in your game.
There are many other useful things that can be learned from in depth analysis of your game, and that you should look for.
Of course, realizing the point at which the game becomes completely lost or completely won beyond any non-blunder induced changes is important too:)
Don't neglect your tactical errors too though. See if you keep missing similar tactical themes.
Also, In each opening you play, there are many recurring tactical themes that if you improve your ability to spot them, your play will improve dramatically (not only in that opening, even if it will be more pronounced there).
Howvfer, after all, practicing your tactics is really the only way to improve them a lot...
Writing all the different ways you can gain from analysis and the different ways to improve at chess is probably enough for a separate forum topic.
It would be nice to see each player saying what method of training/analysis/whatever induced the biggest improvement in playing strength for them, from what level to what level (1300 players need to concentrate on different things than 1900 players, for example) etc... That would be very helpful for many players.