Venice is very expensive, and any place in Venice that isn't as expensive probably is sketchy. (I love Venice, but kind of all of Venice is sketchy, people have to get used to walking out of their 4 mil $ beach-front home and finding a homeless person peeing on it. Seriously.) A 200 sq ft loft half a block from the beach rents for $1500. Yes, that's 200 sq ft, but it's cute as anything. It's attached to the garage of a 600 sq ft house on a tiny lot, both of which are worth 1.2+ mil together. See what I mean by expensive?
It will be hard to find an apt to fit 3 that you'll be able to afford in Venice without good jobs, you're probably looking at a 2 bd for $1600 - $2000, not too close to the beach, or a not too nice building. Be careful of craigslist ads and any deal that sounds too good, there are scams out there. Don't rent long distance!
There aren't very many decent paying (by LA standards) jobs near Venice unless you have a good education. Attorney or doctor in Santa Monica -- because that's the kind of money you need to live by the beach comfortably and most of them can't afford to buy. There are lots of small retail businesses in Venice that don't pay well, restaurants that aren't doing so well due to the economy so they won't be hiring, and your basic Starbucks or fast food type places. It seems like all the steady jobs around LA for those with little experience are laying off or going out of business, like Circuit City. You'd probably have to expand your job search, which means a car might be necessary.
Because the economy is so bad, be sure you bring enough cash for about 6 months, because it may take you that long to find a job that pays enough. Sucks, huh? Also, be aware that LA is expensive overall. A friend from Miami couldn't believe how expensive everything is here, groceries, etc. I wasn't aware, I guess we're just used to it. If you want to move to LA, you might want to look at a less expensive area to start, like the valley.