These are the best accessory any indoor smoker can buy. Ozone generators, Hepa filters, Ionic breezes, etc are nice little add on's for freshening up, but there is no substitute for eliminating the smoke from your environment before the particulate can settle or stir around.
Exhaust fans are rated in CFM - Cubic feet per minute and sones - their relative loudness. These are the 2 important specs to consider when looking at one for your application.
CFM is the real issue in gettin the smoke out. If you have a 10 x 12 room with 8 foot ceilings that is 960 Cubic feet of air. My personal experience has led me to a simple calculation for this size rooms needed "actual" CFM.
1 smoker - 200-300 cfm
2 smokers - 450 cfm
3 smokers - 600 cfm
4 smokers - 900 cfm
Needed being defined as keeping the room from getting nasty.
A typical bathroom fan is 100-150 CFM rated. This can be deceptive as this is "at the fan". If you have long runs of exhaust lines it can dramatically reduce the capacity.
Larger fans can be loud so you need to consider this in your decision. Some of the best solutions are "inline" a fan that can be installed closer to the outlet and 4-6 feet outside of your room buried in a wall or crawl space. These can dramatically reduce the noise. It's important to pay attention to the duct sizing. Getting a high CFM fan (6-900) and installing it with too long a run/too small of pipe can drastically reduce the effective CFM exhaust you get.
Simple solutions can be cheap and very efficient. Window fans do a great job and you can pop them in and out as needed even in winter months.
One consideration seems counter intuitive but makes sense once you think about it, the need for make-up air. If your room is very tight, little egress area for air to get into the room from other parts of the house, you may get drastic reductions in the CFM performance of the fan. Assuming you get a fan with a large enough CFM, your room will go into a "negative pressure" state. This means it wants to draw air from any place it can. Typically this will be through your door cracks, outlets any openings in drywall or ceiling that go to open airspaces in your house. This is the desired state to prevent smoke from getting anywhere else in the house. Get a large enough fan and you will need to either have a damper to open to the rest of the house to get fresh air, or will need to leave the room door cracked a bit to ensure enough make-up air to keep the fan running at peak performance.
Another issue is the existing heating and cooling ducts. Cold air returns are the enemy of a good smoke room. The furnace typically has enough CFM to overcome most fans. What this means is when the A/C or Heat is running your room goes from negative pressure to positive on the returns sucking smoke back into the hvac and distributing it around the house. Blocking the return is a must when you are smoking. I use a garbage bag with a drawstring on the one in my office as it's easy in the drop ceiling. When running my exhaust and when the hvac is not running it inflates like a balloon (negative room pressure). When the hvac comes on it deflates (positive room pressure at the duct due to the cold air furnace power). Closing the heat/cool ducts and relying on the air from the cracked door for fan air make-up has been the "right" solution for me.
Anyway, think of a fan purchase like a humi purchase... it's pretty hard to buy one that is "too big".