When it comes to calves, they should be good to go as long as they've had their colostrum (the first milk right after the mother calves). Calves are born with no immunity, so they NEED the mother's colostrum in order to be healthy. Make sure you ask to see if they have had it. If not, the calves are much more likely to get sick, especially once they leave the farm and get stressed out with re-homing.
Also, when you are checking them out, pick out the ones that look more lively. You want calves that are going to be good eaters, they tend to stay the healthiest. And be sure to check their manure. If it is loose or runny, it could mean the start of scours or another disease. Some of these are easy to treat, others can be deadly. I good healthy calf will have squishy manure, but it won't be like water running from a hose.
You do NOT want the coughing calves! Like I said, be sure to ask if they've had their colostrum, and try to pick out the healthiest calves you see. It would be best to make sure you do your research before-hand, especially if you've ever raised calves before. They are very simple to raise, but if you don't know anything about them then it's very easy for something to go wrong.
If I were going to pick out calves to buy, I wouldn't buy anything younger than 3 weeks old. My reasoning for this is because the first 3 weeks they are their weakest. They are just getting used to their environment, and they are very fragile. If you buy calves that are at least 3-4 weeks old, then you are a little closer to the safe zone. It means they've had a chance to get used to eating out of a bottle/pail (mine eat out of a pail starting around 1-1/2 weeks). It is also better for them at that age, to move them to a new place. Moving a cow stress them out. They like everything to always be the same, every day. They do adjust very well, but during that short stress-time it makes their bodies more susceptible to disease. I'm not saying they will get sick, they are generally fine, but there is always that chance. The older the calf is, the easier she'll adjust to her new surroundings and the moving process.
As for jersey holstein crosses, they are great! I have mostly holsteins but a few jersey crosses as well. They are excellent cows to have, but as stated before, make sure you look at the mothers. They may look great as calves, but the mother tells all when you talk about how she will look once she gives milk!
If you have any other questions, feel free to PM me. I wish you luck and take your time picking those calves out! And the more questions you as about them and their mothers, the better informed you will be.