Where and when should I go what should I do, to save the most lives without sending large changes rippling through world history?
You should go behind your time machine, and pull the power plug out of the wall.
Predicting the effects of causality with time travel is a wicked problem, or a problem with "incomplete, contradictory, and changing requirements that are often difficult to recognize."
But why does that mean you shouldn't go back in time? After all, there's a chance you might save some lives!
Let's look at the two extremes:
Saving maximal lives: 1.2 billion saved
How many lives could you save? According to the World Health Organization, here are the leading causes of death, worldwide:
An estimated 56 million people died worldwide in 2012, most of them by natural causes (e.g., diseases are natural causes. Bullets are not.).
So assuming you do not have a cure for old age or heart disease in your kit yet, let's very optimistically say, maximum, you could have saved ~24 million people in 2015. I have no idea how you'd do that, but there it is.
Now, the population of the world has increased dramatically in the past 100 years, from about 1.5 billion to 7.3 billion. I'll assume the death count scales with population (a bit dubious, but more in-depth analysis would be prohibitively difficult). That means you could save about 1/300 of the population, maximum.
Your best bet might be to bring a printed record of every accident, murder, terrorist attack (with documentation on the attackers), etc. So, best case, assuming everyone listens, and doesn't cause other accidents in the process of avoiding the original ones, you could save 1/300 of the population of every year.
That would add up to about 1.2 billion. (See note 1)
Worst-case scenario: negative 7.3 billion
The Cold War was a very precarious time in world history. There were some well-known close calls, and possibly more that have yet to be declassified and published. However, if your far-reaching life-saving efforts were to cause any "ripples" that affected any of these events (or instigated others), and the US and Soviets unleashed their arsenals, the explosions, fallout, and potential nuclear winter could end life as we know it.
Sure, there might be a few survivors (hopefully your "isolated" kinsfolk have a good fallout shelter and plenty of supplies), but it's an unfortunately plausible worst case.
But what's likely?
As mentioned, causality is extremely hard to predict.
To quote a strangely apt observation from WOPR (WarGames) on the Cold War, which seems to apply to this question: "a strange game. The only winning move is not to play."
In other words, I don't know, but I hope this answer helps to put some bounds on the possibilities.
- I arrived at the 1.2 billion figure by coming up with a rough plot of world population growth, dividing $y$ by 300, and calculating the area under that curve between 1915 and 2015.