Spray booths are mainly to provide a slight negative pressure when spraying paint with organic solvents, e.g. oils or some cleaning products, so you can help vent the small amount of VOC hobbyist levels of spraying generates - so it doesn't build up in your workspace as much. It's still worth wearing a respirator/half mask which can filter organic vapour when you spray oils etc, as you will still get some hanging about your workspace. For cleaning products, just spray them into a cleaning pot with a filter.
Straight acrylics generate no VOC vapour (being as the solvent is only water), only the particulates as discussed above, so there's no need to vent outdoors. The negative pressure will help a bit to contain dust, but frankly I've stopped using mine with acrylics long ago as the effect was pretty minimal. I just put down angled newspaper and spray onto that, while wearing gloves to hold the model. Healthy lungs should be able to expel small amounts of acrylic particulates without issue (the plastic is non-toxic per-se), but it's still worth considering wearing some sort of dust mask, as you would when doing DIY or otherwise generating dust as you're pretty close to the source. I admit I don't tend to bother if I'm only going to be at it for 5 minutes, but I do use my respirator when spraying non acrylics (mostly varnish) or for a longer session.
Assuming you want to carry on using the booth, that foam is way too dense, you want a much lighter piece of foam or filter, ideally source side as firedrake cordova says. I'm kinda surprised your booth didn't come with one, all the ones I've seen had foam (usually blue) on the source side to protect the fan itself. Cooker hood filters are a good source if your booth didn't come with one; the greasepaper one you have on order is worth a try!
Edit: the only toxic acrylics I can think of are yellows/reds made with cadmium, and they're pretty rare these days, especially in acrylics intended for airbrushing. Just check the pot for a toxicity warning for yellows/reds you intend to spray (specifically, a "do not spray" warning). Vallejo used to have some, but they're long gone.
Edited by Arkhanist, 12 May 2021 - 05:46 AM.