DaveyDitzer Loc: Western PA

Sorry, but I cannot completely agree. The 50mm may give the field of view of a longer lens, but not the effect of compression which is especially important in portraits. I've tested this with a nikon crop and 50mm and the portraits were not flattering (big nose phenomenon).

autofocus Loc: North Central Connecticut

Well back in the days of shooting film what was considered the perfect focal length for portraits was from 80mm to 125mm. When you consider the 1.5, 1.6 multiplier on crop sensor bodies the 50 winds up being around 75-80mm, so it does fall into that acceptable range. We've never found "nose problems" when shooting with a 50, but a lot of that may have more to do with your shooting POV. And yes, many like to shoot with longer lenses, as in ~200mm and yes, it does a wonderful job of blurring the background but it also flattens perspective which also can be non flattering.

Friiduh

You already have the focal lengths required to good portraits covered very well.

In a psychology tests it is found that humans remember and recall peoples faces from about 4.5-5m distance. That is the distance that human eye fovea sharpest area, about 2 degree in our total FOV, is covering the whole face. And that is as well a range that where we find face structure very pleasing and comfortable when we are even looking a unfamiliar person, yet closer distance causes more intimate or even threatening perspective.

In portraiture there are few things that are critical to learn, example:

1) The person face has two sides, left and right, and both sides offers different impression of the person. So choose carefully which side you want to photograph.
2) The person eyes and head direction of the camera can be critical, where person character does come out positively or negatively.
3) People control skill is very important, so you can guide them to wanted position and pose that is what you want. The chosen pose is very important.
4) Lighting, a one of the most undervalued things in modern photography. You need at least single flash that is off-camera so you can control its direction and distance of the subject, and/or learning to use available light like windows or sun position, shades, walls etc as your way to shape and direct the light. A good light that shapes the person nicely, is critical.
5) A controlled background and foreground. You should first understand who the person is (status, age, style, expression etc) and then choose the background or the whole environment to fit that personality. Like if you are photographing a 4 year old boy, a sandbox can be great environment, while a strollers not. So you need to get the person in fitting environment and then fitting pose and then move your camera around that location the get the background and scene fit the person.
6) Be prepared to take multiple different kind photos. Wide angle with more scene with the person full portrait, long telephoto for very tight headshots, include heads and hands as they tell more about the person and adds lot to the photo. Get the people relaxed while you move and you get them to move by talking.

The 18-200mm is great lens for portraits as you can go wide and you can go to very narrow. Great head+shoulders shots is easy to with ie. 150mm on that lens.
With a APS-C camera when you are using that 18-200mm lens, and you set it to 150mm range. You get very tight 67x45cm size field of view when your person for portrait is at 450cm (4.5m) distance. I don't remember exactly what F-number the lens gives at 150mm range, as it has f/3.5-5.6 in whole range from 18mm to 200mm, so I guess it was f/5. Now take a measurement tape and measure a such area and think about placing a person head and shoulders inside that. It is very tight.

But at that range with f/5 aperture, your DOF is only less than 16cm! Meaning you will get likely only a single person face in focus. And the depth that is in focus is 7.7cm toward camera from the focus point and 8cm further from the focus point. So if you focus to person face, you get just barely their eyes, lips, cheeks, tip of the nose and jaw in focus, while rest of the head gets blurred.

With a 50mm you get easily closer and you can use that f/1.8 for faster shutter speed to freeze their hands or head movement when in dim light. But you are seriously cutting the acceptable focus depth (Depth of Field) so narrow, that you get easily out of focus photos, or where only single eye is in focus and other is out of focus or person tip of the nose is blurred and so on.

Example: With that 50mm you get from 200cm (2m) distance a about 90x60cm size frame. And if you use it wide open at f/1.8 for fast shutter speed, your DOF is only a 10cm! 4.8cm front and 5.1cm behind the focus point and you have difficulties to get person hands or clothing (status, element, character etc) in focus and even a other eye, nose or lips can fall easily blurred area. So stopping to around f/4-5.6 can be preferred.
And such a wide field of view as about 90x60cm you get nicely person and environment in frame, like hands on table, Some of the background on room, chair they are sitting or leaning on etc. If you back off to 4.5m distance, now your FOV is 200x133cm (2x1.33m) so you get a whole person in frame and you can even fit someone else with them. Or you can get them to raise other leg on chair, rock, handrail etc. With a horizontal shot you get background very nicely with the person so you can fit them to scene like when you go to beautiful place and you want to get the person located in that.

Those two lenses you have covers most cases. And you don't need to go for any other really.
So don't worry about lenses not being optimal thing, instead spend time to learn how to communicate with the subjects, time to do research for lighting.

And if want to spend money, get some cheap off-camera flash. So a nice good small flash, a cheap simple radio trigger and if really going for more serious, a light reflector (a collapsible) that is about 80cm wide when open and about 30cm when collapsed. And what offers you matte white and reflective white, could even work if it is solver/gold for. As you can use that for flash reflector to shoot flash on it and that bounces it back to subject. You can use that in available light to fill light. Or you can even use it as reflector on opposite side of the bare flash. So get a nice book about portrait lighting with simple manner and get creative.

There is no single lens out there that you don't already have, that would magically make your portraits better.
On and have a friend or someone who is willing to spend with you a couple hours to test and try all kind poses, framings and lighting setups.

Once you know how to operate the camera, you know how to modify the light and control the subject, then you can get more demanding situations like uncontrollable person in a uncontrollable situation. But you start to see the available light, possible situations and changes to get the shot.
And be very prepared that there is no single setup you can use for everyone. As every person faces and bodies are different, their clothing is different and their character is different. So you need to change all in the setup to get the look. Some people has tiny noses so you need to get closer to make it look "normal". Some has huge nose, so you need to get it look smaller (ie. Raise camera, longer distance, get them look upwards to you etc) and some has bodies that needs "fitting" and some needs "filling" and you can change all those by their pose directions and their hand positions, legs positions and angles etc.

portraiture is 99% of everything else than what you have in a camera (Mpix, sensor size, lens, F-value etc). And you can set everything else perfectly and only then to raise camera to take the shot. Or you can raise camera and start taking shots and fail in every single photo when everything else is wrong.

Edit: As addition, you will eventually hit to the trendic theme "ultra shallow DOF" where people talk about the beauty of the blurred background and how you need a small F-value lenses to get that. There is a well known secret, there is two things that people should talk when they talk about such photos. 1) Blurred background 2) Out of focus person face.
As those are two different things, and many want to offer a smaller F-value lens like typical 85mm f/1.8, yet it will only cause half of the face out of focus, while background is somewhat blurry. Compare that to 50mm f/1.4 that has even less of the face in focus, but even less background blur. And then there can be some other settings like a 200mm f/3.2 that has most blurred background, but as well deepest focus range so your person face is completely in focus. So if someone wants blurry background, they shouldn't use small F-value but long focal length. if someone wants half of the person out of focus, they should use a small F-value.

Friiduh

Many has challenge to understand the light, and you just brought up the point.

There is only two kind light; Soft Light or Hard Light. That is the character of the light. And you really need to find the position between those two extremes that is fitting the person. Some works with hard light (small light source or light source further) and some works with very soft light (huge light source or light source very close).

So the key thing in that is to control the size of the light source (bare light bulb/flash, reflector, diffuser etc).
Some modifiers can be more both, like some softboxes allow to shoot through and yet they diffuse the light as simultaneously.
Then there is simple things like using a black reflector, to deepen the shadows and cut contrast, compared to white reflector. But it is all about those two things, hard or soft :D

autofocus Loc: North Central Connecticut

I know manners are becoming a thing of the past, but a thank you would be nice