Now that your decision to bring home a second dog is made, the next thing is to decide on the kind of dog that would fit well with your family and your current dog.
The first step is to evaluate if your dog is dog-friendly. If you are not sure, then begin with introducing him to other friendly dogs in a safe play area. Reach out to a friend whose pet is known to be calm and friendly and arrange for a supervised play date.
There are places that facilitate supervised play whose help you can take to make this evaluation. If he is absolutely not comfortable with other dogs then you might want to hold off on the second dog and work with socialising him.
If he is friendly, then what you need to look for in your second dog is not the breed. When choosing the dog, consider the size of the dog. Would you have enough space to house two big dogs? If you get a smaller dog, will your over active lab be too overwhelming for the small one? The question you have to answer is then “What size suits you the best?”.
Next thing to evaluate is the temperament and energy. Choose one with a temperament that best complements the temperament of your lab yet playful enough to be a good play companion for him.
Introduce the identified new member gradually. Make sure you introduce them in a neutral territory - one that will not seem as an intrusion to both dogs.
Once they are introduced, take them for a long walk.
As for the possessiveness of your labrador, it is your responsibility as a pet parent to teach him to respect you and trust your decision. Worries about divided attention is a projection of your emotion and has nothing to do with the dog. Scale up on your leadership skills and establish rules that both of them will have to follow. Invest in some quality time to train them and you can enjoy the undivided attention of two dogs.
(Consult a professional trainer who can help you with the introduction and training.)