Diamond here probably has all you need, but I also own and use 3 relatively inexpensive chess programs. Fritz is very powerful but a little nonintuitive to learn how to use. HIARCS has very human like play and the database function easy to use, although since it's limited to PGN files, you end up shuffling DBs in and out. ChessKing is delightfully quirky, but has loads of fun exercises. You should probably google them and check out their websites. Or you might just want to go the free route. I have Scid v. PC but I'm not motivated enough to bother learning how to use it. There is an active community of users here though if I wanted to. Lucas Chess has umpteen features that I likewise haven't explored, but I do like playing against some of the more stupid programs it contains. Sometimes if you're a little depressed it just feels good to beat the snot out of an engine! Hope that gives you some names to google, and of course you can always do a "search forums" here. Many previous threads on the subject. Have fun!
Best Overall Chess Software?
I am considering getting either diamond or platinum membership here. I assume you think it's worth it, IYO?
Yeah I'm always shilling for the site. 
I really do think that ChessMentor is a wonderful tool for learning chess and the new Tactics Trainer over at V3 has some great new features. Because I'm old and have to pound stuff into my head over and over again, I need the diamond just so I can continue to review old lessons. The 5 lesson a day limit on platinum won't do for me, but obviously your mileage may vary. And while you can find plenty of videos on youtube, these are of higher average quality by far. I would even go so far as to say IM Danny Rensch's Live Session Videos alone are worth diamond. So yeah, I think it's well worth it. I'm not rich by any means, but I really don't mind spending a little here on chess. In truth though, for those folks just scraping by, you can find plenty of free stuff on the web to help you get better at chess. This is just a lot more convenient, and probably more efficient as well.
I am probably more interested in game analysis after I played my games, than other videos. Although those videos/lessons wouldn't hurt either, I suppose.
Does the game analysis feature provide explanations for the moves, or just moves themselves?
Erik would shoot me if he knew I was typing this, but if all you want is game analysis you don't need diamond. Scid v. PC does good analysis and it's free. There might even exist another popular chess web site where you can send PGNs of your games and have them analyzed. No, Chess Mentor is the main reason to go diamond. Very few programs provide explanation like the old Chessmaster did though, but it's not hard to click through alternate lines and see why they're better.
@baddogno's comments are helpful. He is correct to say Chess Mentor is very useful. Also the instructional videos on chess.com are only available with a Diamond membership. These are well worth having access to. Many of them are excellent.
As for game analysis using software, for any of these you have to learn how to use the programs, and if you do not already know how to use them it can be a pain, as searchng the internet to find exactly the specific instruction you need on how to perform the various tasks can be a laborious, time consuming process (this is my experience - yours may vary).
Chess.com's analysis softare is ok to check for mistakes and blunders. It provides only minimal commentary in this regard (blunder, mistake, etc) but does suggest moves that it considers better in these cases. So it is useful, if minimalist.
Also note that you can try out any premium membership for free for 30 days (i.e., a full refund within that period if you cancel). Also you can cancel any premium membership at any time and get a prorated refund. Also you can subscribe on a month-to-month payment schedule as opposed to paying the yearly rate (which of course is cheaper).
All in all, I consider $99 for a yearly Diamond chess.com membership to be a very good deal, considering the time, energy and money you could spend elsewhere trying to duplicate all its benefits.
A slight correction. It appears from the marketing blurb on chess.com's membership page that if you cancel a premium membership after the 30-day free trial period, you will only get a credit, and not a pro-rated refund as I had stated.
http://www.chess.com/membership?c=navbar
I recommend to check out Chessbase first as the reference standard for all chess software products. There is more instructional content on the internet for using their products than other similar products. (I'm not affiliated with Chessbase)...
Here is a sampling of stuff available on the web that might give you some ideas...
Choosing a chess engine.....I think the consensus is that Komodo 9.3 is currently the strongest chess engine...followed by Stockfish (free)
http://en.chessbase.com/post/john-hartmann-and-then-there-were-two
http://komodochess.com/Komodo9.3-48a.htm
note that when you purchase Komodo directly from the company, they do not provide a GUI with it. However, Chessbase will sell you Komodo with a Fritz GUI....
http://shop.chessbase.com/en/products/komodo_chess_9
and Chessbase 13 is the best chess database program/package...
http://shop.chessbase.com/en/products/chessbase13_starter_package_engl
scroll through this list for specific articles of interest...
http://en.chessbase.com/search?pattern=chessbase%2013
Chessbase products channel on YouTube....instructional videos...
https://www.youtube.com/channel/UCgbqH06jfCDCqAZtNahWLYg
Steve Lopez' videos on chessbase products are always good, if not entertaining. Unfortunately he no longer works for Chessbase (I think he left about a little more than a year ago). However, the fundamentals he discusses are in most cases still germane and applicable to the newer versions of the products....
https://www.youtube.com/watch?v=uNa398Nfm2w
Check out the Imperfect Chess channel on YouTube...seems to have one of the better instructional video collections relating to Chessbase products...
the first video has some audio problems...(in my experience with it)
https://www.youtube.com/watch?v=JaSFQrdIn7s
https://www.youtube.com/watch?v=3NzVU12_1jM
IMHO Lucas Chess and SCID vs. PC are the two best chess software programs available and they are both free. If you don't know how to use them go over to YouTube and you will find plenty of "how to" videos. Also available on YouTube is a great collection of chess videos that explain all aspects of chess. The best things in chess is free. And having gotten all these things for free I can now afford a membership in chess.com because that's the best place to play chess.
How useful are chess mentor lessons and videos on chess.com? Do you use them often? Are they helpful?
Thanks.
I do not use chess mentor lately but I have in the past and it is very good. I have also watched the videos on chess.com in the past but have not done so lately. The ones that I have watched are all very good, very instructive but there are tons of free chess videos on YouTube so you might also want to check those out. Also I liked Dan Heisman's videos on ICC.
What are some opinions on Fritz. Is it a stand alone program? If I get it, am somehow obligated to subscribe to something else? How easy is it to use to just analyse games or make suggestions if I'm tying to learn a new opening for example. Any opinions are appreciated.
How useful are chess mentor lessons and videos on chess.com? Do you use them often? Are they helpful?
Thanks.
I have used them both and feel that they are useful and helpful. How often you should use them is up to you. Obviously, the more you use them, the more you will improve your skill at chess.
Yeah, with youtube, chess.com, chesstempo.com and a good chess book on strategy(positional techniques), you should be able to grow as far as you can. Never underestimate a little chess club/over the board playing(even OTB tournaments if you can).
For a book, I recommend spending a few months in this one
It isn't a book, as much as an amateur's Chess Bible. 'Reading' the book wont make you 1600, but studying it fully, and applying the strategies to your basic game. It really has become a never ending process for me. I think I should be able to build up to 1700 using this book's material toolset. I'm a slow mover though, and sometimes I don't play chess for long periods of time.
Study strategy, do tactics, play games. You can get to 1500-1700 just doing that. 1800-1900 usually takes some 'time', most of us will probably never truly be 2000+ Not that you can't. I've seen some younger players get from beginner to 1900 in like a year or 2. Having a huge, super absorbent mind helps haha Mine is more of the smaller sun dried type.
but yeah, standalone software is sorta a thing of the past, I still have chessmaster 10. I also still have chessmaster for NES ha
I am an intermediate chess player (1400+ rating here on Standard Live) looking to improve my game. I own several instructional and game collection books and one on openings and endgames (I own fewer than 10 books in total).
I am looking to possibly get a chess software program that provides game analysis, explanations and openings and any other features I cannot think of right now.
Does it make sense to get any chess software programs? Or is paid membership here enough (I don't have one now)?
All opinions are welcome! Thanks.