Brand and variety of alfalfa seed?  I would use the same brand and variety of alfalfa seed, whether it was no-till seeded (or direct-seeded, as some would say), or whether the ground was tilled and seeded that way.  We don't change seed choice based on seeding methods.

Brand of drill/ equipment?  John Deere no-till drills are popular here.  However, I also see Great Plains, as well as other colors.

To me, the bigger issue is seedbed preparation.  Previous crop - as well as management of previous crop - is important.

What is the previous crop? corn?  what happened with the corn stalks? were the corn stalks harvested, or were they left on the field?  removing corn stalks is a plus, if you are going to no-till seed a crop with a small seed such as alfalfa.   Having a small grain crop previous to seeding alfalfa can make a nicer seedbed to plant into. No-till seeding into soybean stubble can work, as you have less residue to deal with, compared to a previous corn grain crop.

What kind of chemicals were used in the previous crop? make sure you aren't using a product which will have carryover.  But, then this applies when seeding with tillage as well.

I like the improved soil-seed contact that you get with no-till seeding, and I think that is the big plus for the practice.