The pot itself won't make as much a difference in time to boil as the energy source and amount of water used. If you want a pot to come up as quickly as possible, you need an induction hob. Large quantities of liquid will take a while, no matter what the energy source.

I use a 10 qt pressure cooker with a clad base and an 11 qt stockpot with clad base (Ikea $15!). They do a fine job.

Stock pots are one place that paying a premium isn't going to give you a big return in responsiveness. I would find the least expensive in my target capacity. Vollrath's range goes quite large, being a commercial product, and it has a nice thickness of aluminum. You just want to make sure it fits your hobs well so that the heat is distributed across the entire bottom.

Because as alex says, "Stock pots are one place that paying a premium isn't going to give you a big return in responsiveness" I use a 8 qt Cuisinart stock pot for most stock pot uses, which has a multilayer base but is light weight for its size. It does the job it's supposed to do. I don't remember how much it cost but it was very affordable. Most of my other cookware is Demeyere and Le Creuset.

Thanks @alex9179 and @ChristyMcK

I believe the size is what's going to be key. I think my existing stock pots are probably adequate for actual stock production, but I likely need a Vollrath, Sitram, Berndes or other low and wide piece to maximize heating on my current gas range. Like true stockpots, they are tall and narrow and probably aren't too effective with the existing range but likely it's not making a big difference in those usages (one is a Cuisinart as well -- the one that claims to have a layer of copper but I know was probably inexpensive).

I have a portable induction unit, but it's really no better than the range due to the power limitations of a regular AC socket.

ETA after the fact to add more comments

This post was edited by gooster on Mon, Jan 12, 15 at 16:30

I am following up to write that I stuck with my existing stockpots and instead picked up a braisier from Sitram Catering. It's mid-height and has a nice thick copper disk bottom.

I'm just wondering whether anyone has encountered something like this in searching for stockpots:
A stockpot that has a spigot that facilitates emptying. The spigot would have to be high enough on the pot so that some vessel could be placed under it, but low enough so that the heaviest portion of water, stock, or whatever is in it could drain. It would have to be leak proof over time, therefore not susceptible to heat degrading the spigot seal. It is getting even more difficult for me to carry filled stockpots, pasta pots, canning pots, and so forth back to the sink for emptying.