Don't under estimate how much they will smell. I would try to get the biggest fan/carbon filter you can afford-that's going to be hard to do for under 100-150bucks. Remeber that smell has been the ruin of many a grower.
For 80 bucks I would look into Ona gel, bucket, and 9" fan(like a desk fan). It really does work wonders. It doesn't just mask the smell, it binds to it and helps it 'fall out' of the air. It's strong stuff-it was made for sewage plants. They have a fresh linen scent now that doesn't smell like a gas station bathroom, I would recommend that one. I personally use a combination of carbon filter, ona placed right outside my grow room, and some strategically placed timed misters. Sounds like overkill but my house doesn't just not smell like bud, it smells clean and fresh. I actually get comments about how 'clean and fresh' my house is. I keep it that way intentionally. Everyone thinks I'm actually a responsible adult!
You can put a little ona in the bottom of a 5gal bucket that you have drilled a bunch of holes in. Then, on the lid of the bucket, cut out a circle for your 9-10" fan and place it in there. The fan should be blowing down through your bucket so all the air in the room is constantly being forced through your bucket and all around the ona gel inside.
I would not recommend putting it inside your closet. Your finished product might take on an 'ona' taste. For 80 bucks I think it's your best option. The small ona gel costs about 30-40 bucks where I live. The work really well for about a month, then start deminishing. I always have a back up on hand just in case.
I would also recommend timed 'misters'. There is a product called Ozium that really works well, but galde and febreeze make similar misters. The ozium is a much better product for eliminating odors, the glade and febreeze just maske them, but either way since they are on a timer the odor control is continuous. You put the mister on a wall(I like to put them right by any doors people might come to, and right outside the door of my grow room) and you can set how often you want them to mist. I use the glad ones by my front, side, and back doors and I use an ozium mister right outside my grow room door.
Hope this helps, those are the cheapest options I have come across that actually work. Just always make sure you have at least one back up of each. Smell has a way of creeping up on you. I will never make the mistake of not having a back up carbon filter or ona gel ever again.