Seconding trade - it really doesn't take time to 'do it right' though if you want expertly optimized trade, I would avoid eve trade altogether - you;re still in competition with wily, well equipped and tenacious opponents, just with an interface facilitating that conflict 'less directly'. Optimal output, therefore, is unlikely.
There is exploration content that requires no pve, but this is the least rewarding (and most accessible), which ironically makes it over farmed, hard to find and unimpressive. Good sites in null and low will almost always require pve, unless you go for ninja mining (gas or ore). Becoming some form of junker/'rogue trader' in the cluster could be fine, if you intersperse your days with rp on top.
As for grim darkness - that is what sells unfortunately. On the flip side, I consider it the 'marketing material' and by no means indicative of the realities. People live, grow up, have kids, grow old and pass on in eve as in other fiction-worlds and life. I assume with all of the heart ache, fond memories and such. Like people who only ever watch war-news, frontlines documentaries or disaster coverage, we capsuleers are force fed the very worst, and perpetrate a lot, of the cluster. It doesn't need to be like this, but I prefer the joys and good days of rp to be shared in small groups of friends - broadcasting your joy on a public outlet just seems a little out of place (I rp caldari if you didn't guess...).
As a brief example, Ael has fired maybe on two occasions, both storyline missions, and only then to win favour with her patron megacorporation during her Sukuuvesta citizenship application. Since then she has funded, directly or indirectly, Caldari war efforts as well as start up companies, mostly from the comfort of her freighter, office or homestead. Grim darkness is there, I'm in the arms business with a personal axe to grind after all, but a lot of the time is business, lounging with friends and talking of 'the good old days'. She's a creature of comfort, has been of means from a young age and likes to 'share the wealth' albeit in the form of entertaining her guests instead of wasteful philanthropy.
EVE will always have the aspect of conflict, but you can skirt it's edges, providing social commentary, enabling it or whatever you feel like doing, but as a non-combatant you will be taking the 'hard road' for acceptance and brotherhood in a community of hardened killers, mercenaries and idealists who feel that though the pen may be mightier than the sword, a pen with a bayonet attachment is mightier still.