I know from experiance that plastic tends to hold flavors from previous use. My belief is that it won't make a whole lot of difference in the wine except that the beer buckets can leave some odd flavors in wine.
It is real easy to become overcrowded with buckets and a lot of folks have a bucket for wine primary, another for wine secondary, same for beer, plus a couple to rack into and maybe one with a spigot to bottle with. Next thing you have 8-10 buckets and maybe a few glass carboys also.
I would go to your local school cafeteria and bum a used food bucket (strawberries, blueberries,etc, NOT pickles or any other acidy food) these can be cleaned/sanitized and become disposable. Don't keep the buckets too long after different beers/wines have been in them as they will impart other flavors to wine. This may not mean much if you are serving it at a block party but in a competition or trying to impress the inlaws it might make a difference. Buckets are too easy to come by to keep using the same ones over and over. Having said that, my very first beer attemptwas made in a used 90 wt gear oil bucket, cleaned and sanitized. I have learned a lot since then. I buy 5 gallon glass bottles for 5 bucks off the bottled water truck.