Devon me boy, those are all great pipe dreams. In order to capture paint particles (over spray) you need an air velocity of 100-150 feet per minute velocity. So lets say you build a booth that is 2 feet high x 3 feet wide, or 6 square feet. To maintain the required velocity you need a fan that will move 6 sq feet times 500 feet per minute velocity or 600 cubic feet per minute, and that will need to be at a minimum of 2" static pressure. Bathroom fans don’t even get close.
The static pressure requirement is to overcome the pressure drop across the filters that will need to be no less square footage then the entrance to the booth. Filters need to be equal to the best filters you would buy for your home for air purification. The filters need to be upstream of the fan and have a reasonable transition from the square shape of the filters to the round shape of the fan inlet (for least pressure drop.
Next the fan needs to be a squirrel cage type fan, preferably a backward curved or radial tip type tip to get the static pressure needed. The backward curved fan will be quieter than the radial tip.
This is a thumb nail description of what is needed for an efficient paint booth or hood. I would recommend doing some research online to see if there is anything available for booth/hood design information. My books are currently packed or I would sketch out a rough design for you. I promise you will not be satisfied with a ‘bathroom fan’ design in the long run. Home made can be cheaper, and sometimes better than store bough if they are done right.