Yes, you're looking for Acrylic Gesso, I've seen it in Black, Gray and White. Liquitex is a good brand, but even generic ones work as well.
It's really cheap and will last you a lot, I haven't had to buy any for over 60 models, and the bottle (About 2 oz) still has about 3/4.
Gesso really starts to shine when working in sub-assemblies, as any spot of it you accidentally remove or need to repaint can just be covered without having to lose the rest of the paintjob.
It also can be used in pretty much any weather, although compared to spray primer it can take a bit longer to dry.
Speaking of drying, gesso shrinks whilst doing so, making it very hard to obscure detail even with a sloppy coat, experiment a bit and find the ideal amount of thinning on your gesso so it is not too thick but still thin enough to dry in a reasonable tine.
It doesn't take much experimentation to find the consistency you prefer to work with.
Now, for your question on art store acrylics.
Most artists' acrylics aren't formulated for going too thin, so their pigment and medium is somewhat thicker, as they are intended for opacity as opposed to miniature detail.
You could technically use art store paints for minis, I have used them before, but it takes a lot of thinning and fuckery to get them in shape.
The colours may be a problem, as most hues are intended to be mixed by the artist, so if you want consistent colours , that may be a problem
Then there's the stuff that just like everything, the better stuff is usually expensive. Dollar store acrylics may be cheap, but their pigments are of horrible quality and generally not good even for canvas painting.
In my experience as a canvas painter, I'd rather use Vallejo or Gw paints for minis, as it's less fiddly, and good acrylics come almost twice as expensive as most hobby paints.
I'm not saying that you can't paint with other acrylics, but imho, I'd rather spend my time working on my backlog than making my paints workable.