Best way to evaluate the possible moves in games?

I have always heard checks, captures, and threats. Granted in the opening you would focus on developing. I just had some thoughts I wanted clarification on?

1. With regards to checks I know you should not check just because you can as it might not be your best move. What do you use to determine if the check is the best? Obviously if it leads to a gain or a mate you should do it.
2. When it comes to capturing if you can get a gain I can understand why it makes sense, but if it is an even trade how do you know if you should capture and trade. It is my understanding that if you are down you should not trade as it leaves you with fewer pieces and your opponent keeps the advantage. 
3. Threats come from creating something I assume your opponent should or must respond to that can allow you to gain material or tempo? I also assume it means you can threaten something more valuable than a piece of yours under attack. 

I might have posted something incorrect and if so I apologize but what exactly do you look for I know I miss stuff in games. 

It seems you're asking about the non-tactical elements. The one most worth mentioning is piece activity, which is some combination of mobility (influencing many squares) and being in contact with important points (usually either weak pawns of either color, or squares near the king of either color).

Pawns and kings are typical targets because such weaknesses tend to be long term.

So that was a nice segue into pawn structure and king safety... authors of strategy books will include additional elements like control of a key file and the initiative, but if all you knew were those 3: piece activity, pawn structure, and king safety, you'd pretty much know it all. Control of a file and initiative are natural extensions of piece activity anyway.

That's a bird's eye view of it... it may not completely answer your question, but people have literally written series of books on strategy so it's hard to fit into a forum post.

I guess the unspoken connection to your OP is that tactics and strategy blend together during a game. Like you said, you don't check just because you can, you do it because it wins material (tactics) and/or improves the piece itself or some other element in the position (strategy).

Checks, captures, and threats are emphasized because some low rated players focus on a very good strategic idea... they play 5 high quality moves, and then lose a rook on move 6.

Well, if you're down a rook... or more to the point, if you're blundering a piece every 5-6 moves, then you're going to lose no matter what... so the first big hurdle is developing good calculation habits by focusing on checks, captures, and threats. After that you can improve your results by weaving strategy into the mix... of course you can learn about strategy any time, it's just it wont improve your results much at first, not until you have good calculation habits.