In choosing someone to create a portrait, check their website for examples of other work to see how you like their style. If you want a realistic yet brushy, painterly work (for example) do not choose someone who does more photorealistic paintings and vice versa. If budget is an issue, ask your preferred artist about less costly options (such as a drawing, sketch or just the head) instead of a larger piece that incorporates more of the body, detailed background and complicated jewelery or clothing.
Ask the artist for testimonials (or look for them on their website) to see what previous clients have to say about their experience.
An artist will generally have a range of choices at different price points to choose from, depending on the complexity of the idea, size, medium, subject or finish (a sketch would be much less expensive than a complex composition with many details for instance).
It is important for a client to feel confident that they will be satisfied and happy with their painting. It takes some trust to commission something when you don't know exactly how it will turn out. Make sure the artist will include you in the process, showing you photos or sketches of what the painting will look like in general. I always show a number of options (that I know will make a good painting) so the client can choose the general expression and composition to suit how they see the subject.
Once you have carefully chosen your artist and been part of the process of designing the piece, let them do their thing, knowing that your painter guarantees your satisfaction and is committed to creating the absolutely best painting possible.
You also should ask about care after the painting is completed and advice on framing. I always offer to varnish the portrait painting of my human subjects after at least one year (to allow time for all the layers to dry completely) at no cost, as a service to my clients.
Don't miss this interesting article about selfies vs. painted portraits (with some additional tips on how to choose a portrait painter to create your cherished heirloom)!