I just finished one and a few lessons learned.
I'd go with the freezer. A freezer doesn't have to work very hard to hit 38 degrees, a fridge does (did that)
I'd build the wooden "collar" with 2 x 6 (I used 2 x 4). The hinges for the freezer will likely be a tad longer than a 2 x 4 can handle for all four screws.
If you plan to go for four 5 gallon kegs, you might want to cut out four keg sized 8.25" circles when you go freezer shopping to make sure you can cram four in there. So people think you're crazy, so what? You're a homebrewer, they should expect it.
One word: Craigslist