If you are seriously interested in GOOD portrait photography or better yet. really FINE portraiture, background management is important.
There is more to it than most casual or non-portrait shooters think. It is quite a bit more complex than black, white, or gray.
The function of the background is to isolate the subject(s) on a non-distracting field but yet add colour or tonal masse which provides separation, and dimensionality. The appropriate background for any given shot can also prove texture, suggest environments, and help create the "environment" or the illusion thereof. The background, properly toward the end with lighting and the clothing colour or shade can also help create the desired KEY.
It's difficult, for me, to recommend any specific style or kind of background unless I know what kind of work or style you aspire to produce. There are commercially available backgrounds start for seamless paper, to various kids of multicolored and painted backgrounds, to elaborate scenic backgrounds and in some cases, you can make, improvise or paint your own backgrounds. Any given background can be rendered in various ways depending on how it is lighted, the distance between the background and the subject, the degree of depth of field or lack thereof, and the focal length in use as well as the camera to subject distance.
Someof the common mistakes are using a painted "old masters" kida background and trying to simulate an oil painting- it always looks artificial. That same background can be used to create a masterpiece if it is used subtly to provided colour mass and separation with just a hint of pattern or texture. The same applies to a scenic background- it is used flat out in detail it can look artificial. If it is light properly and somewhat out of focus, it can suggest the environment and not look like a stage backdrop.
A good reliable supplier of photographic backgrounds is Denny Manufacturing. Here's a link:
https://dennymfg.com/They have many hundreds o styles sizes and materials- portables, studio, and big cyclorama the background that roll right down and over the floor.
Some commercial backgrounds are GAUDY and artificial-looking, but if used with some savvy, many of those can work.
If you are gonna start with a single background, I would recommend a multi-coloured brushstroke kinda model in a predominantly cooler colour blues and greens. That is because colder colours bring out the warmth in skin tones and provide better colour contrast. A warm background can provide a more monochromatic feeling.
You will need a size that is wide enough to handle individual portraits, couples and groups. If you intend to shoot groups and full-length portraits, you will need one with enough height as well.
What kinda lights do you have or intend to purchase? That would help in making suggestions and discussing background lightg specifically.
For pure white or black or any specific colour, you can use seamless paper.
Check out the Denny online selection and tell me/us what you prefer. I can tell you how to best use it.