You think there is no violence at LA games? I think you had better google Bryan Stow.
Actually, provided you sit in some decent seats (i.e. away from the gangbangers), you won't be hassled much while in the stadium. DEFINITELY take off your team's gear and hide it in a bag before going to the parking lot, though. Some people just get straight up assaulted from behind for wearing the other team's gear.
Before the game isn't as much of a big deal, because no one is drunk yet.
I wouldn't jump the gun with buying tickets for the NLCS. While there is likely more demand this year than other years (due to the opponent being the Cubs, and LOTS of Cubs fans living in LA), the prices should still go down between now and game time. You can plan your trip and book your flight, and then just buy tickets off StubHub the day before.
That's what I would suggest.
Keep in mind this is unprecedented territory being that it's a Cubs series, but also keep in mind that I got EXCELLENT NLCS seats against the Cardinals in 2013 for about $150 each. Equivalent seats to this same game were over $300 just a day before that.
Keep refreshing Stubhub when game time gets closer. There is zero point zero chance that it will fully sell out on there.
Regarding where to sit, do NOT get seats in any of the following areas (these all suck):
LF Pavilion
RF Pavilion
Top Deck
Any Reserve level ticket not labeled "VIP"
Any Reserve level ticket with an aisle # higher than 32
Any Loge level ticket with an aisle # higher than 156
Any Field level ticket with an aisle # higher than 45
Loge level row P or behind
Field level row S or behind
Also keep in mind that the obnoxious foul fence is in front of aisles 1-14 (and parts of 15 and 16), if you're splurging for field seats.
My favorite seats (and honestly best value) are field aisles 15-24, rows A-H. Those are padded, as well.
Dodger Stadium is a classic-style stadium built in the mid-1960s. It is not super old school like Wrigley or Fenway, but it has a lot more charm than the newer stadiums. I personally really like the place.
Buy parking on dodgers.com beforehand to save some money.
Anyway, the most important advice I can give is to wait on Stubhub until 24 hours before game time.
Prices will especially fall if the Dodgers are behind in the series, ESPECIALLY facing elimination.
You will likely get the worst deal for Game 3, and the best deal on Game 5 (provided no one gets swept, of course).