Well....
You could start by reading this;
https://www.techspot.com/vb/topic133075.html
Beyond that there are 3 current Intel sockets,; LGA775 (all c2d Celeron, Pentium dual core and current Core2 Quad chips, LGA1156 (core i5, (core i3 to be released),
and LGA1366, which is high end Core i7.
I know squat about AMD, and I'm not willing to learn for you.
Well, I know this, you can't put an AMD in an Intel motherboard. But see, you already knew that.
So, you could only upgrade directly with an Intel CPU. As to compatibility, you would decide on a CPU, then visit your motherboards' website, and search CPU compatibility charts specific to your particular board. The charts will tell you if the CPU you've selected would be "plug and Play". or require modification via a BIOS update. You could obviously research this in reverse by picking the board first and reading the same list.
For your rambling question about, "are all boards created equal", don't believe it, it's a myth about men and motherboards.
The rule of thumb is that the later the date of manufacture, (or release), the more CPU are generally compatible with any given board.
Depending on which motherboard you have, it may be possible to achieve a performance boost through "overclocking" your processor.
Since gaming performance depends a great deal more on which video card you have, you could always overclock a bit, and upgrade your video card. For this you should also consider upgrading the power supply.
lenghty question but thank you for any answers and please excuse the horrible spelling
About the spelling, verily I'm on board with your assessment of horrible. In "lengthy", the "t" goes before the "h", but in fairness you had all the letters right.
As to "upgradeing", we almost always drop the "e" before adding "ing". If you want to agonize over spelling, (personally I enjoy doing so), make sure spell check is turned on in Firefox. Oh, the "U" should be capitalized, because it's in the title, not to mention it's the first word in the "sentence".
Did any of this help?