I'd say if you're having trouble not to use lacquer - why take the risk? However, you did not specificy what kind of lacquer thinner you're using. Lacquer thinners made by Tamiya and Gunze are much milder than anything you'd buy in a hardware store - the odor is very mild. (Lacquer and acrylic paints are somewhat in the eye of the beholder. Check the label - if the paint has warnings on it that it is poisonous and flammable, you have a lacquer paint even if - as is true with both Tamiya and Gunze paints, they're also called acrylic. On the other hand Tamiya and Gunze paints are also much milder in oder than say Alclad.)
Below is a basic division of types of model paints.
Lacquer paints (see Alclad)
Solvent based Acrylics - Tamiya and Gunze are prominent. Think of them as kind of lacquers and they certainly spray best with Tamiya or Gunzer lacquer thinner (either thinner works fine with either paint). The agent (the stuff that suspends the pigment) is a mix of solvents that will include ISP among other things. Pigments are made with dyes. (Because dyes are liquid, Tamiya is a very "user friendly" paint for airbrushers because ground pigments can help clog airbrush tips along with drying.)
Water based Acrylics - the agent is mostly a liquid polymer that is water solable. These will include Vallejo, LifeColor, Revell Acqucolor and artist grade acrylics like Golden. (I don't use MMaster, so I'll let others fill in that blank.) Except for artist grade, there are conditioners, levellers, mild drying retarders etc mixed into the agent. Vallejo has Model Color (thicker and made for hand brushing but easily airbrushed if you know what's up) and Model Air which has a much thinner polymer and (I'd guess) more additives. All of these paints claim to be non-toxic. That said, because many (I can't testify for each type) use mostly or entirely inorganic pigments (ie: naturally occurring). The pigments themselves might be harmless to your stomach, but things like zinc are not good for the lungs. (These are pretty rare - I admit that I rarely use a mask, but that doesn't make me right.) But regardless, water based acrylics are odor free and non-toxic. They all can be thinned slightly with water, although I'd use Vallejo airbrush thinner on any. (Some people find Lifecolor challenging with airbrushes and maybe their brand thinner would be better.)
I'd like to give a plug for Golden High Flow Acrylic paints. If you can ignore the lack of specifically military colors, these are fantastic paints. They airspray neat perfectly and hand paint very well. (Golden Fluid acrylics are better for hand painting. You need "Airbrush medium" from Golden, Liquitex or Vallejo to airbrush them - the same stuff is the key to using Vallejo Model Color. It's very heavily thinned polymer and white in color, although it dries clear. Use it and you won't over-thin you paint - if you do, that's trouble with any water based acrylic.) The finish is excellent. There are about 45 colors and include some artist specialty things like transparent shades. However, several are "mixing colors" and if you get a kick out of messing with paints, you can create just about anything - and these paints are made to mix.
Vallejo has a YouTube video online called "Acrylic Weathering Techniques" which is an hour long and shows how to paint and weather a model using nothing but acrylics. There is now a much more detailed book from Vallejo of the same name.
If you're doing cars, I'd guess you'd want a smooth finish. I can't promise the same results with water based acrylics than with lacquers. However, if you check the uber-guru Paul Buzik's YouTube Channel (recommended for everybody who has a model - the guy is one of the flat out smartest and effective tutors I've seen) you'll find a section on priming models which he claims is the secret to smooth finish. He prefers spray guns to airbrushes - those aren't cheap. However, some auto parts primers fit the bill perfectly. Duplicolor and Napa both have spray can lacquer primers: look for "sandable" and "filler" on the label - and be wary of any claims to quick drying. I've used Duplicolor Gray and it's great. The stuff has punch in the odor - but unless you're in Alaska or in the middle of a global warming heat wave, put on a rubber glove and use it outside. It's dry to touch within an hour, but I'd give it at least twelve or 24 before going further. Anyway, the stuff has excellent coverage but is coarse - which means it fills minor seams, scratches etc extremely well. Use a very fine sand paper and carefully give it a light sand, and you have a near gloss surface. (Obviously, experiment with sheet plastic or a "medical experiment" model before you use something new on your more expensive kit.) I'd guess if you combined lacquer primer in a spray can (outside - and done in one minute max) with water based acrylics you'd get excellent results with in a much friendlier environment.
Eric