Please Explain Mutants & Masterminds 3E Combat/Powers Interaction

tl/dr: Mutants and Masterminds for Dummies?

A Savage Worlds (Necessary Evil) campaign in which I have been playing is wrapping up, and the group decided to move to Mutants & Masterminds (3rd Edition) for an entirely new campaign in an entirely new system.

I’ve read good reviews of M&M 3E, so I’m game. I just learned Savage Worlds, after all, I come from a rules-intensive background (Hero System/Champions).

I’ve also read the M&M rules here a couple of times. And I’m not getting it, despite its being based on the popular D20 system, which is described as easy and intuitive (I don’t know d20 either).

Since I still don’t understand how to play, I can’t intelligently make a character, and pressure to get started is building. Accordingly, I have been Googling around for hints on how the game actually works. So far the examples people breezily spin off are, in fact, not enlightening. In one case the someone explained:

Uh, aren’t “save values” a large part of what defends you? That’s what I thought I understood. So how does “stunned doesn’t decrease save values. It just means you…have a lower defense” make any sense?

And then there’s this cogent explanation from another site:

I am **utterly baffled **as to where “vs. 27 (for strength)” comes from. So I showed this example to someone in my group, and got this reply:

I don’t get where “Base 15” comes from.

I’ve seen that there are some fans of M&M on the SDMB. Would anyone be so kind as to walk me through the basics of M&M 3E combat…and perhaps provide some non-basic examples, since a Microsoft-style “simplest possible example” typically leaves a lot of questions open. My objective is to get enough of a feel for the system that I can make a useful, smart character, not one based on misunderstanding and misinterpretation. I’ve seen such misunderstanding result in cases of massive frustration.

Also, our GM tackled the “stunned means lower defenses” question (see below), but admits he is trying to interpret the rules. Is his interpretation correct?