In my opinion this is a good idea. Keep it simple at first. As your positional understanding, technique, and tactics improve expand your opening play accordingly.
Low Level Openings
I suppose it might somewhat defeat the purpose of choosing an easy-to-learn opening, but on the off-chance that it is of interest, there are about 100 pages on the Center Game in Dangerous Weapons: 1.e4 e5 by Emms, Flear & Greet (2008).
https://web.archive.org/web/20140627091711/http://www.chesscafe.com/text/hansen109.pdf
There are about 100 pages of material on the Center Game in Dangerous Weapons 1e4 e5. However for a player of my skill a lot of the material is not relevant. About 50% of the material deals with Andrew Greet recommended 8.Qg3 Which is was originally played by W.S. Viner in the Australian Championship 1913. It is one of 3 lines White can choose from on the 8th move. I like 8 Bc4. Which also isn’t very relevant as none of my live chess opponents have staid in the book for eight moves
About a third of the remaining material deals with hypermodern type moves by black, which my opponents also don’t tend to play.
The rest of the book deals with different early moves choices that black might make. To me these seem reasonable but so far I have not seen them.
In light of the above, I wonder if it is worth while for me to develop a response to common non-book moves made by my opponent? For example an early Qe2?

Okay, so a couple key things.
Firstly, a majority of your opponents will play moves other than 1...e5 after 1. e4! So you will need to develop other lines against those openings. You need to have answers to:
-the Sicilian
-the French
-the Caro
-the four main lines of Scandinavian (2...Nf6, 3...Qa5, 3...Qd6, and 3...Qd8)
-the Pirc/Modern
-the Alekhine
So just saying you want to play the Center Game is not enough. But maybe that's not your point anyway; you may just be asking about those two openings.
I don't have a great opinion of the Center Game, as I think black achieves equality rather easily. But if you know it well, that's still okay! The better player (on that day) should win, and the games will be interesting to analyze.
The Scandinavian can be a fine opening. But which line are you trying to play? 2...Nf6 or 2...Qxd5? And if the latter, then where do you move the queen on 3. Nc3? All the options are viable but it is important to know what you are doing in some depth.
Best of luck with these openings!
Remember guys we are talking about D and C class players so too much detail is not important but just focusing on development and being careful to avoid blunders. :)
I want to thank everyone for their comments, they were quite useful.
I believe that chess down here in the Bog, (live chess with people rated mostly below 1200) is quite different. I realize that I only have a limited number of games but this is what I have experienced so far:
I have only seen two responses to 1 e4, 1… e5 and 1…d5. I have yet to play black against anything other than 1 e4. In most of the games the Queen comes out early, between move 2 and 5. Most of the games are decided by who makes the fewest or least serious blunders.
My biggest challenges is visualization. It is hard for me to see all of the consequences of my move two moves out, I seem to be poetically good at setting myself up for a pin. Currently I am practicing tactics in a book, to improve my visualization. Any recommendations to help me in this area would be great.
I have been learning the Center Game Opening in the hopes that I will regally get to a position that I understand better than my opponent.
@ Five of Swords, I have played through some master games with the Center Game. My model game if you will is: Winawer vs Steinitz at Nuremberg in 1896. I like Winawer’s game because it demonstrates a good attacking motif.
One question I have is: If I notice a non-book move is made by my opponents frequently, for example 3….e7, should I spend the time to develop a 5 move or so response to it? Kind of like adding another variation.
... If I notice a non-book move is made by my opponents frequently, for example 3….e7, should I spend the time to develop a 5 move or so response to it? ...
I've always found it very difficult to prepare for a move like 3....e7.

3...e7 isn't a possible move, regardless of the position! I'm sure you meant something else...but in any case, if you don't know what to do in the opnening, development is usually the way to go. If you're having specific problems, post them here.
You are right 3...e7 would be hard to prepare for. Guess I shouldn't try to type early in the morning
What I ment was 4...Qe7
As in the following
1 e4 e5
2 d4 exd
3 Qxd4 Nc6
4 Qe3 Qe7

8.Bc4 looks very good for Black after 8...d6, but in any case, it should be better than the 8.Qg3 gambit line, which was busted by GM Avrukh a few years back via a very powerful exchange sacrifice:

I like the logic of setting up an opening for white and an opening for Black. I started this way: I will play 1.e4 when White and 1....d5 when Black. I then commenced playing lots of blitz games to get a feel for the common responses to my moves.
Slowly you will get a feel for what openings you prefer. Then you can study up on some major systems for your repertoire.

if u like scandinavian Qxd5 and Qa5, why not playing same with white?
1.e4 e5 2.d4 exd5 3.Qxd4 Nc6 4.Qa4!? (most tell ?! but seems overoptimistic for black).

Common flaw I see from all beginners.
You think the Center Game is easy because you remember the first 7 moves after one look at it. BUT DO YOU UNDERSTAND THE FIRST SEVEN MOVES???
Remembering them doesn't mean sh*t if Black deviates anywhere from moves 1 thru 6!
For example, which "7 move line" do you know like the back of your hand?
After 1.e4 e5 (Black can play 1...c5, 1...e6, 1...c6, 1...garbage) 2.d4 exd4 3.Qxd4 Nc6 4.Qe3, already Black has 3 major options. 4...Bb4+, 4...Nf6, and 4...g6.
Your problem ain't solved!

why thrillerfan, are u always so agressive and so tough about openings?
4...Bb4+ just tranposes into Nf6 followed by Bb4 (after Nc3).
And on g6, White plays same way, with Nc3, Bd2, 0-0-0, and can think about h4 too...
Ok black has many options and move order, but less than ruy lopez...

why thrillerfan, are u always so agressive and so tough about openings?
4...Bb4+ just tranposes into Nf6 followed by Bb4 (after Nc3).
And on g6, White plays same way, with Nc3, Bd2, 0-0-0, and can think about h4 too...
Ok black has many options and move order, but less than ruy lopez...
Trying to reiterate that all of those low rated players that think they know it all because they have memorized 8 moves of a single line (Like B351a2 of chapter 6 of some random book). People at this level should not be studying openings because they don't know how to study them right. They memorize rather than understand. And at their level, nobody they play against will have the slightest clue what the "book move" is at each turn, and if they play a "book move", it's sheer luck!
So after you've spend hours memorizing lines in the Center Game, and Black has deviated on move 4, don't you now wish you spent those 200 hours that you spent studying the center game on tactics and endgame play, especially after you drop a Knight on move 12, and the following round you have a drawn Rook ending but proceed to lose?
Stick to opening concepts, and make better use of your time studying what you should be studying, not openings!
I am considering an opening repertoire (if you can call it that)
Consisting of the Center Game as White, and the Scandinavian as Black.
What I like about these openings:
They are easy to learn (understand) I remembered the first 7 moves of the Center Game after playing through it once.
They seem to have a common strategy.
At my level people actually play these, possibly because a lot of the moves seems naturally consistent with opening Theory.
Is there any issue playing these between 1200 and 1500?