Unless that brisket has a substantial fat cap on it, it's likely going to be dry. Most of the markets that sell brisket flats trim nearly most or all of the fat off of them. If that's what you have, I'd cook the brisket in the oven using some kind of braising liquid.
If it does have a decent fat cap, go ahead and give it a go. If all you have are the three woods listed, I'd go light on the mesquite, or better yet, get some oak, pecan, or hickory, all of which go great with beef. I really don't pay attention to time, but rather focus pulling the meat when it's done. You're in the ballpark when the meat reaches 180 or so, but that's just a basic guideline. It's done when you can stick a probe through the meat and it slides in like butter, not a minute sooner.
Here's a link to my first brisket, using Bigabyte's excellent tutorial, which is linked at the bottom of my thread:
Try and find yourself a nice packer, follow the tutorial, and you'll turn out a fine piece of meat.