There are two basic types of Black Sex links. One type is made by crossing two standard breeds, say a Rhode Island Red or New Hampshire rooster to a Barred Rock hen though others can be used. These tend to be good dual purpose birds, they inherit those traits from their parents.
The other type are the commercial hybrid layers. These tend to be small, say leghorn size, so they don’t provide much met. But they are laying machines. Do you know which type you have? If you know which hatchery they came from and what they are called you can possibly determine which they are by going to the hatchery’s website. Hatcheries tend to use names like Star or Comet for both types so those names aren’t much of a clue by themselves, but matching name and website you might be able to figure it out. A big clue is usually the weight of the adult chicken, which some hatcheries give.
So your goals are eggs and meat, as well as wanting to sell the chicks. No rooster will make commercial hybrid layer offspring good meat chickens. That’s just not why they were created. If your BSL are based on dual purpose breeds, about any decent dual purpose rooster will create decent dual purpose chicks with them or your Barred Rocks. I know a lot of people get really hung up on breed, breed, breed. I don’t, not with hatchery chicks. I just don’t see that much difference in productivity between the dual purpose hatchery chicks.
I do see a lot of difference in the hatchery chick roosters. A few years ago I got 18 Buff Rock cockerels for a hatchery, Ideal to be precise. I’ve done the same thing with other hatcheries with the same results but I’m giving a specific example. I got those cockerels to get a new flock master with the others going to the freezer. Out of those 18, only three met my criteria for my future flock master. The rest were eliminated, most were too small or slow maturing by comparison. A couple were big enough but did not have the behaviors I wanted. This same type of thing happens with cockerels from other breeds from other hatcheries. The same thing happens with cockerels I hatch from my flock. Some are better quality than others. If you want to improve the quality of your flock I suggest you get several cockerels so you can select the best for your breeding program. The rejects cook up quite well.
Since you want to sell the chicks, I’d suggest you consider a Barred Rock rooster. People tend to like to buy purebred birds, but this means you will need to separate the hatching eggs. You will not be able to tell the difference between the chicks from your BSL or BR hens at hatch and probably not later.
Another option, but only for your Barred Rock hens, is to use a rooster that will give you black sex link chicks. If you go to the very first post in this thread and look at the second chart you will see what roosters will make a black sex link chick. Any of the roosters on the left in any group will work with a BR hen. But again, you’ll have to separate your BSL eggs from the BR eggs when you hatch. Any chick with the white spot will be a male from the Barred Rock hens but the ones without the spot could be from either hen.
Tadkerson’s Sex Link Thread
https://www.backyardchickens.com/forum/viewtopic.php?id=261208
This does not meet your criteria for improving your flock so much however. Once you make a Black sex link, it cannot be used to make any more. BSL’s are a one generation only thing.
That’s my opinion. We all have our preferences and personal opinions. There are other things that could affect this, but these are the things I’d consider.
Good luck!