"I have no idea where to begin."

The place to begin is with your ductwork. If your duct from the hood to the outside is too small for the amount of cfms you will need, you could buy the greatest hood in the universe, but it will be more noisy and less efficient due to the ductwork. Most hoods require an 8" or 10" diameter duct. What do you have?

With respect to cfms, for a Bluestar it would be great to have a hood with 1000 cfms, but then you run into the issue of makeup air. Depending on where you live, you will need makeup air for anything more than 600 cfms, and some localities it is 400 cfms. A 600 cfm hood will be adequate for most things other than grilling, or things like making a steak in a cast iron pan which generates a lot of smoke. If you feel your cooking does frequently generate a lot of smoke, you will need to go up in cfms, and get a makeup air system. Makeup air is a complex subject, so do a search online about it.

Make sure your wood hood enclosure is deep enough to cover the front burners. The hood should be at least 24" deep front-to-back. It would be a problem if your hood was, e.g. 20" deep because it would not be covering the front burners.

Your life will be a little bit easier if you get a metal hood rather than a hood inside of cabinetry. A metal hood means you do one-stop shopping, and don't need separate cabinet enclosure, liner, and blower. A metal hood will be a little less expensive as well. Since you have made the decision to buy the powerful Bluestar, you need to buy the accompanying hood powerful enough to handle Bluestar's btus. Sometimes people buy powerful ranges, but then say they want to spend a minimal amount for the hood. That won't work.

You can go with a 1 piece. My parents had their old hood wrapped with cabinetry to match. But they already had what they needed since their original cooktop had an indoor grill (that was never used). If you have an indoor grill or high output wok, you’re going to want a high CFM to clear the smoke and grease. Makeup air isn’t an issue in my climate, but is when the interior temp differs significantly from the outdoor temp (you can’t just open a window, for example).

Best products are also very good. Wolf OEMs their downdraft, which is what I have. You don’t need the brand name, there’s no Wolf logo visible on my downdraft or the controls.