I too was in the same boat (only I had the Canon 18-200) looking for a second lens. The 18-200mm is a great jack-of-all-trades (and nothing gets from wide to close faster, making it a good choice for when you need to travel light and get the shot at an event), but it can come short with image quality, bokeh (what you’re after in your portraits), and low light performance.
So, when I went lens shopping two years ago… I ended up purchasing a 50mm 1.8 and a 10-18mm 4.5-5.6 (they came together in a kit).
I was definitely wowed by the sharpness of the 50mm. I would often leave it on my camera instead of my 18-200. I also loved the bokeh, and it definitely performed better when I was taking pictures of my little siblings. It even became my go-to flower lens (I eventually was gifted a set of extension tubes, which added further value to the lens).
After a while, I wanted something with a little more versatility (and a wider angle so I could shoot groups easier), so I ended up going with the Canon 17-55 2.8 IS (which is a great quality zoom lens).
My 50mm is my second-most used lens in my kit (the 18-200 is the least used at this time), and is my go to lens for flowers and individual portraits. It’s a fantastic value for the price.
All that said, you should probably ask yourself what kind of portraits you’re looking to shoot. If you’re shooting groups or full body portraits, you might want to consider something wider like around 24mm. If you’re photographing kids running around, you’re going to want a zoom lens. If you’re shooting headshots primarily, you might like something a little tighter like an 85mm. If you have no clue, the 50mm is a pretty good bet.
(p.s. if you want to try something for a while before you buy it or only need it for a specific shoot, I’ve used LensRentals a couple of times [and if you use my referral link here you and I both will get $25 off 🙂 ]: https://share.lensrentals.com/x/KbHDTP)