Honestly, any PvP is unwelcome for me and even though I love SF, I won't play EvE for that very reason. Any zone that has any Non Consensual PvP is PvP zone no matter how rare it is. This is a binary choice.
EvE is justifiably proud of it's PvP. It is the biggest selling point to many of the people who play. It is hardly surprising that they don't really court PvE players. It's shame that the only really big SF MMO that is not licensed is dedicated to piracy, murder and corporate thuggery, but that's what the payers want I guess.
Admittedly, I have only been ganked in high-sec space *once* in several years of playing Eve Online. But the main solution is "don't AFK autopilot between systems" and "don't open containers that are not your own".
And that is your high sec security sorted.
Low Sec: More of the same, also pay attention to local chat
0.0 space: More of the same, pay attention to alliance/corp chatter as well (I highly doubt you would be in 0.0 space solo)
Wormholes: Pay attention, remember that Local chat channel is delayed for updating by 15 minutes (unless they speak), keep eyes on the back of your head.
But honestly? Unless it changed a lot from when I played, just random ganking in High Sec space was rare (notable exceptions being Hulkageddon/Burn Jita) unless you managed to piss someone off.
Side note: There is Eve University which is a player ran corp which accepts newbies to the fold, and helps them out learning the game, whilst being in a relatively safe environment. Bonus points: As far as I am aware, there is also the unspoken rule of NOT war-deccing Eve University (or at least there was when I was playing), or you will get some rather larger alliances/corps dropping their stuff to make your life unhappy)
side note 2: Some people would consider the market game as PvP... I am sure that some of those players would sell their mother if it would get them a few ISK
(and it isn't uncommon for some people to buy up all stock of something in one area to manipulate the price in their favour. THis is one thing that happens when you have a location based market, along with *everything available is made by the playerbase*