Do you already own the van or are you shopping for one? Is your goal for this project saving money, saving the earth or projecting an image of saving the earth?
Bio-diesel can mean a few things. At one extreme, it can mean waste vegetable oil, which is filtered used vegetable oil which had the advantage of being recycled and basically free. But most cars require fairly extensive modifications to run it, especially in all but the warmest climates. Also, in most places there are now companies that collect the waste oil and make it into commercial fuel products so, alas, the days of free fill-ups behind the burger joint are over. In some places you can still get WVO at a significant discount, but that really depends on where you live.
The terminology has settled on when you say “biodiesel” you mean diesel that is produced on an industrial scale from some sort of biological sources. This is usually sold either completely pure (B100) or in some mixture with regular diesel, usually 10-20% (B10 or B20). Most newer diesels can run the blends without modification, but only some can run B100. The cost and hassle of converting a non B100-compatible diesel varies from model to model, but newer diesels are generally pretty complicated. You won’t save any money with biodiesel and like constanze said, there are also some big questions about how “green” it really is (although I find it interesting that over in Europe biodiesel is seen as the big boondoggle and ethanol looks promising, whereas the exact opposite seems to be the prevailing wisdom in North America).
LPG and CNG are not as popular as they once were for a few reasons. Firstly, back in the days of carburetors, you could do a conversion in your garage. These days, to end up with a vehicle that will still pass all the various inspections you pretty much need to get a professional conversion and they ain’t cheap. The fuels also used to be significantly cheaper, but these days the price difference between them and gasoline usually hovers right about at the break-even point where the cheaper fuel cancels out the reduced mileage. The other big advantage they had was they were a lot cleaner, but with modern emissions controls on gas engines they’re no longer significantly so. The only thing they still have going for them is that the fuel almost all comes from the US and Canada, if that’s something you care about.
It doesn’t scream “look at me, I’m saving the Earth!” like alternative fuels, but realistically going with a 7-passenger minivan instead of a full-size van would be a lot better than any of the above.