As for separating the new soil from the old. The only way to completely enclose the new raised bed with some type of impermeable membrane. The cheapest and easiest of these is plastic, but you stated you don't want to use that. Anything natural, like the burlap or mulch you mentioned is going to wick up water from the soil below it. Along with the water will come the toxins (at least some of them...not all toxins are water soluble but many are). Also mulch or burlap will decompose in a few years and the plant roots will make their way into the contaminated soil below.
A more permanent way to separate the new soil from the old would be to cap the old soil with cement or concrete and then build the new raised beds on top of that. This is a pretty serious step though and not really the way I would go in a home garden.
A in between solution might be to fill the bottom of the bed with gravel. You'd want a pretty deep layer, maybe 6-12 inches. On top of the gravel you would need some type of liner...burlap could work here although it will break down over time. The liner would just be to prevent the new soil you add from washing down into the gravel and filling all the spaces between the stone. The gravel layer would create an physical gap between the old soil and the new soil, reducing the chance of water migrating upward from the old soil into the new bed. It also creates an inhospitable zone that plant roots would be less likely to grow through.
A different option would be to do some bioremediation on the contaminated soil. There are various plants and fungi that will accumulate toxins in their tissues or break them down. You can then harvest and remove the contaminated plants, removing some of the toxin with them. Other toxins volatilize and can be greatly reduced by repeated tilling and turning over a year or two period. Other toxins are not going to be effected by either of these things. So again you really need a soil test and some knowledge of what you might be dealing with.
Upholstery businesses, clothing manufacturers, goodwill and salvation army dumpsters (they throw away clothes that need mending).
But there's no need for anything more than newsprint, unless you know the below soil is contaminated, a barrier is not going to fix that problem, and your planting will suffer. Most local colleges will provide cheap soil tests.
Also, what are your standards? What do you consider 'contaminated' ?
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!