...was wondering how safe it is to airbrush indoors?
Not to put too fine a point on it, but it would be impossible, or at least impractical, to airbrush OUTdoors. It is radically finer than a rattle can and the slightness breeze will ruin your day (not to mention dirt and insects).
Not having airbrushed before, does it give off a lot of fumes or particulate? I'm obviously concerned about health but also wonder how messy it will be to work inside.
Subjectively airbrushing produces far less particulate and fumes in the workspace compared to a rattle can (where the majority of paint never sees the surface of your model). That said, there is still over-spray (more or less depending on your technique) so you have to deal with it. Exactly what you do depends greatly on the paint and/or solvents you chose, your relative concern for getting the work area dirty etc.
Your first line of defense is to wear a respirator, and one with the correct cartridge for what you are spraying, and you will want to do so even with a spray booth because virtually none achieve 101% particulate and vapor capture (about 1 in 100 DIY booths I've seen meet this description and surprisingly few of the "hobby" booths on the market do either). Beyond that its a question of what you are spraying and how badly you need to get it out and/or capture it.
In the case of solvent based paint, including (in descending order of noxiousness) lacquers, enamels, and alcohol base acrylics (including Tamiya), you'll definitely need something to get at very least the fumes out
safely, if not the particulate as well (note I underscore "safely"....lacquer thinner shot into a bathroom fan is NOT safe).
On the flip side if you use one of the growing number of popular water (solvent free) acrylics, and you are tolerant of a dirty room, you may need nothing more than a respirator since there are no fumes, only paint "dust" (quite literally, that's what you have 9" out from an airbrush with water based acrylics). I use Vallejo ModelAir exclusively and have no spray booth or extraction system. I wear a 3M 7500 series respirator with P100 cartridges and after a few models every horizontal surface in the room needs a good wipe down. :) While I do use an alcohol based cleaner, I use a clean-out jar with charcoal filter next to an open window so no issue there.
