Need more info on what kind of portraits you are shooting and how many people in them. Are these environmental portraits of people at work? Someone with an arm casually on the barber chair in their shop? Someone actually cutting hair, pausing to look up and smile at the camera?
F1.8 is a very narrow DOF, so you will have some out of focus shots. Are you working the shoot for an hour trying to get one perfect photo, or do you have lots of people to shoot and you need to make every shot usable? It really sucks to have a great shot you can't use because the focus was just off enough because you shot at f1.8.
I do Santa photos in a mall at Christmas. I use at least two lights, one on a huge umbrella as a main light, then one on camera set a stop or two under to fill in a bit on the subjects face. I keep in on camera because I move around a lot to get a good shot. A third light for the background helps too, and sometimes I even add a fourth for a hair light on the subject if their hair is blending into the background. Nobody likes a photo of someone in a dark room.
I shoot all my Santa photos with an 18-70/3.5-4.5 on a crop body. Most of the time I'm shooting it at the 45mm+ range, unless I get a large group, but I rarely shoot it wider than 28mm if I can help it. It's just too easy to make people look bad with a wide. I'm also not capturing much in the way of the subjects environment. Sometimes we switch to shooting in a sleigh and then I use a slightly wider lens, but I'm a big fan of capturing smiling faces in my portraits, so I need a reason to shoot loose or I'm zooming in a bit.
I NEVER use a tripod because there is almost never a need when you are shooting with strobe. The strobe is plenty fast enough to stop the action while you shoot handheld so that you can adjust you shooting angle for a good shot. Don't cripple yourself with a tripod, just leave it in the car. Rather keep that camera to your eye and actually look through the viewfinder and move you and your subject around until you find that perfect angle that makes them look good.
Unless you want sterile looking shots with a plain background, use the interior of the barber shop as your background. If you are shooting at the chair, remember it moves and set it where you need it so the background works to set the scene without taking away from the portrait. At indoor distances, f4 or f5.6 will usually add enough blur to the background so it doesn't take away from the subject, but retains enough detail to set the scene. Resist the urge to just step back and capture the entire room with the subject plopped in the middle.
How are you going to blend the available light in with your strobe or are you going to shoot over it? Remember they are different colors? Nothing sucks as much as a well lit subject in a green or amber room or dark.
The color of the available lighting will not match your flash (unless you put a colored gel that matches the ambient color temperature on them, but just don't go there. It's way more hassle than it's worth and you don't have a color light meter anyway.) An easier way to do it is shoot over the available light so it doesn't even show up in your photo. This may mean turning off as much of the available light as you can, unless you light a nicely lit subject in a green or amber room.
To get away from the ambient light and it's color, you will probably end up shooting at the fastest shutter speed your camera will sync the strobe at. (this is another reason you don't need a crutch...I mean, tripod.) You also don't want to shoot at f1.8 or you are sure to capture that off-color ambient light.
Most of my portraits are head and upper body. Think a kid on Santa's lap, or sitting with him in a sleigh. Sometimes it's a family of 5-6 and it becomes a challenge to line up faces so I see more smiles and not the lame old 3/4 body shots some photographers default to when it's more than one person in the shot.
Most of my portraits are taken in the f4-f5.6 range. That gives me enough DOF to ensure every shot I take is usable and I only have to worry about capturing a great facial expression to make a sale. Nothing sucks like being unable to use a great shot because of a technical problem with it. If you have all day to shoot and only need one perfect shot, then sure, shoot at f1.8 if it floats your boat, but I'm doing this to produce images my client love, not produce shallow DOF "art" to stroke my own ego.
You are going to have trouble with that 50mm prime as well. Primes are very limiting tools when you are doing portraits. When I was a newspaper photographer and sent to do an environmental portrait of, say, a musician, heck yes I shot with my primes. I carried a whole bag of them from 20mm to 300mm. For the job you describe, I would hate to walk in with just a 50mm lens on a crop body. If you have a wide zoom, even if it is just a kit lens, make sure you bring it.
Keep it simple. Part of taking a good portrait is putting the subject at ease and making them comfortable with the project. Don't shoot them first thing in the morning, nobody looks good just out of bed. Consider some music, keep things lively, be confident and don't fumble with your equipment. Don't take too long with your subject or it may tire them out. These aren't professional models. If you see the subjects smile die, stop shooting, ask them to shake it out or relax, take a quick breath and reset them with a new smile. This is where the ability to keep the subject as ease and make the shoot fun is at least, *IF NOT MORE* important as any photographic skill you may have.
I'd not set up anything too complicated or try to redesign the room too much. Work with what you have for a background, position your subject where you need them, use maybe a few props from the room and have fun.
And remember sometimes less is more. Maybe all you need for lighting is a single strobe bounced off a ceiling/wall/corner of the room behind you. I've made a lot of really nice portraits this way with one simple bounced light. I used to velcro a piece of pale green or amber gel over my strobe, drag my shutter a bit and use the available as my main light with the strobe to fill in.
Anyway, I'm sure most of this advise seems random and a bit vague, so keep the questions coming. Or google "how to shoot an environmental portrait." And good luck with your shoot.