Superman in the ring, Round 1
The second issue of Superman features a story where Superman rescues the life of the former heavyweight boxing champion of the world who was drugged by his former manager and wound up down and out. Superman impersonates the boxer (Larry Trent) and eventually helps Larry regain his title and expose the men who took advantage of him.
Sports corruption must have been a prominent concern in the late 1930s; just last issue, Superman pulled the same trick, disguising himself as college football player Tommy Burke to root out a corrupt coach. While I do have some problems with Superman being this master of disguise, I can believe that maybe he wasn't such a perfect likeness in these stories, but merely good enough to fool audiences at a distance (remember this was before television).
It's interesting to see Superman wasn't always busy saving the world, though he always was the champion of the little guy.
The second story, 'Superman Champions Universal Peace!' is definitely a war era Superman story. It involves a deadly gas that is stolen by war profiteers. Superman follows them to a small war torn nation where he's determined to stop them - and the war.
This is a great example of how early Superman stories did not soft-pedal things. This one story alone features animal cruelty, murder, Superman lobbing bombs and destroying buildings and a manned dirigible in flight, Superman threatening a villain with 'cracking your head like an egg shell will be messy', Superman standing by while a bad guy dies of poison gas, and the state doling out capital punishment!
Superman also isn't an all-powerful god here, either. He nearly loses his balance and falls off a plane (remember he can't fly at this stage), and is later knocked unconscious by an exploding shell. Call me crazy, but I prefer Superman this way.
And I should mention that Joe Shuster's art here is really great - he's not just the first Superman artist, but should be remembered as an artist of some distinction as well. He's at least as good, and probably better than most guys working adventure strips of the time!