I recently came back to gaming after taking a decade off, so I'm with ya on the quest to find non-violent, less "intense" games.
Here's my two cents:
Steam is a good place for purchasing games.
I second the assessment of Portal being a bit intense. It is a great game, though.
Here are games I've enjoyed that fit your criteria:
Minecraft is amazing, once you get into it (better if you have someone play it with you and explain it).
Braid
Don't Starve
FEZ
Gone Home
Limbo (violent player deaths, but super fun)
Monaco
Mark of the Ninja (cartoon-like violence, but an amazing platformer)
Trine 1 & 2
If you're looking for a first person shooter type, I hear that Bioshock Infinite is less intense/violent/evil than the first two, but I haven't played it yet. (I'm queazy; I couldn't handle the first Bioshock. Way too intense.) Perhaps others can comment on whether or not Infinite would be okay.