That's awesome you are starting a veggie garden for the first time!
Oscar Cotton wrote:I'll be using a cedar raised bed
What do you plan the length, width and depth to be? How many raised beds are you thinking about building?
Oscar Cotton wrote:I'm not sure about the condition of the existing soil and if there are any toxins present
Is it possible to ask the previous owners if they used any pesticides on the property? That would be my main concern. Unless you live in an industrial part of town, heavy metals like lead and mercury shouldn't be a problem (not always though!). Don't plant your veggies within 5-10 feet of the perimeter of your house to avoid any old lead paint that might have found its way into the soil.
Like previously mentioned, the only way to know for sure is to have your soil tested though. If I was in your situation and could afford it, I would definitely have it tested.
Oscar Cotton wrote:I'd like to avoid plastics or other synthetics, because I don't want it leeching into the new soil
I definitely understand your concern in this realm. However, most plastics only break down and leech material when exposed to UV light. I'm sure there will be SOME particles that would leech from a plastic liner buried the soil but I'm guessing that the amount would be very minimal, maybe even unmeasurable.
If it turns out there is a serious toxin issue in your soil, you would be much better off with the plastic liner than risking contamination. The food grow above a plastic liner would still be FAR better for you than even organic vegetables from Whole Foods, etc., in my opinion. Other than concrete (like Chris already mentioned), plastic liners are the only other thing I can think of that would completely eliminate the chance of contamination.
Instead of growing your vegetables on the ground, why not build 3 or 4 elevated raised beds like the one below
Using the Square Foot
Gardening method you could get a good amount of food from four elevated raised beds like the one above. The best advice I can give you, in general, is to start small and build slowly year after year. Biting off more than you can chew can often lead to disappointment and a loss of interest. Expect to make mistakes and plan on learning something from them. Like many people have said, you learn more from your mistakes than successes. But most importantly, have fun! Good luck this growing season!