I wanted to buy a large stockpot for canning tomato sauce and be able to use the same pot for the double purpose of beer brewing. I'm considering Update International Stainless 40 Qt. stockpot. It has stainless encased aluminum base to make thickening sauce less likely to stick. Does this sound like a reasonable solution? I also would use the pot to make meat or vegetable stocks which I freeze ahead in portions for later use.
Brewer here. Yes, that should work fine.
Material-wise, you want stainless steel so there is no leaching of metal when you start to boil, and no break down if you use chemicals in it later for cleaning (don't ever leave any chemicals in the pot though, follow directions, many chemicals will even eat away stainless steel if left too long). Either stainless steel or aluminum can handle the heat. Stainless steel encased aluminum pots actually tend to heat more evenly though (not much of a concern when brewing), so that's nice.
The only consideration you have is size. 40 qt. is 10 gallons. Most intro batches of beer are 5 gallons. This would be perfect for a 5 gallon batch. If you mash (as opposed to extract), you will collect about 6-7 gallons of wort (pre boil). This will boil off leaving you the amount you want. See where I'm going? If you up the brew from 5 to 10 gallons, the next most common homebrew size, the 10 gallon pot is not big enough. There are tricks to get around this though, such as boiling less liquid and topping off with water to desired amount, but having less liquid affects hop utilization (not too big of a deal on a homebrew scale though).
So, I'd say if you're just starting out, this pot size is fine. It will get you through intro size (5 gal) and will even work at 10 gal, depending on how you do it and what you want to do. Anything bigger, you'll probably want pro and/or dedicated equipment.
With respect to cooking, pretty much any thick-bottomed stockpot is going to get the job done, that one included. For a pot this big, I'd try to also make sure you like the handles, since it's going to be really heavy when it's full of liquid.
You probably also want to pay some attention to the dimensions: