Booner is spot on. Vallejo is my primary, but I also use Tamiya paint. I do a lot of armor, so I have MIG, AK, pigments, washes, oils, etc. It all has its place and don't feel like you need them all at once. As time goes by, your paint collect will expand of its own accord. And don't forget the primers and dullcoats! Those things really help.I will, with the utmost respect to all, most politely disagree.
The difference between craft paint and hobby paint is the size of the pigment in the paint. Hobby paint has larger pigments and perhaps a thicker 'carrier' that when applied to a figure can hide detail. I use acrylic paint for a number of reasons, the first is it's water based so I can thin the paint with water, clean my brushes with water, use water to retard drying, etc. When I first started painting figures 40 some years ago, acrylic were kind of new to the hobby, most painters then used either oil-based paints, or enamels. Now most have gone to acrylics. I never liked the idea of using a petroleum-based solvent to thin or clean the brushes due to the smell. And I'm largely self-taught; I never took art in school so everything I learned was from some wonderful magazines that used to be available. Now you can learn by looking at You Tube.
The specific paints I use are "Vallejo" which are kind of pricy, but they also have another line called "Model Color" and I don't notice a difference in the quality between them, other than the Model Color might be a little less expensive. Games Workshop also has a line of paints also called Games Workshop. These paints are more intended for role-playing figures, but I really like some of their colors. The company "Citadel" also make a line of colors, and I have some of those. When I first started in the hobby, I used a paint called "Polly S" which went out of business or changed their name years ago. Pretty much any paint you can buy from a store that caters to the role playing, "Dungeons and Dragon" crowd will work. But what I think sets the acrylics apart from oils and enamels is that they dry flat, where the others dry with a gloss or sheen that to my eyes, just doesn't look correct. Look again at the picture you posted of the large diorama. I'm assuming the Union troops were painted with enamels as their blue jackets and kepi's have a glossy look to them. When was the last time you saw wool with a glossy sheen? In most of the painting your going to do, you'll want a flat color because most of the clothing you'll be painting were made with natural fibers of either cotton or wool. In those few times where you want a glossy look, you can either add a gloss overcoat to the flat undercoat, or you simply buy a gloss color. The one difference maybe in a flesh color. With the natural oils on our face, a little sheen there is ok. Or maybe the hair on a horse, or some leather.
I'm pretty hard on mine and the finer the brush, in terms of how many, or few hairs it has, the faster I wear them out. I've got a few that are called "Short Liner" and are 18/0 and 20/0. the bristles are very fine, but also very short, so the paint on the brush dries out quick so I only use them for the finest detail work. I probably use brushes in the 1, 0, 00, and 000 size the most. They normally have synthetic fibers, as I find I wear out something like a badger hair or any natural hair brush pretty fast. These brushes have very fine points, but don't be afraid to trim them a little for your application. I also have a few flat brushes, and I think they call them a "shader" brush. I use this to help blend colors together and for dry brushing and when it starts to wear out I use it for I'll call "grinding." It's sort of like dry brushing, where you load the brush up heavy with paint them rub most of it off on a rag and then lightly run the brush over the figure. My "grinder" technique is somewhat similar except I'll actually use the brush and push it hard into the surface of the figure. It's good for shadows, adding a 5 O'clock shadow to a face, or by varying the pressure and layers you can make a pair of leather leggings looked like the color is fading from a dark green to a lighter one as you paint up the leg.
Of course natural lighting is the best, then incandescent lighting, but when I paint at night, I'm finding I'm using LED lighting more. I find that I paint for awhile then stop and come back the next day for a critical look of what I've done the day before. I give the paint 24 hours or so for it to fully dry, even though acrylics dry to the touch pretty fast. I think a 24 hour drying period lets the paint cure and come to it's true color.
There's a lot of miscellaneous stuff to this hobby, and maybe that's one of the attractions for me. I use Yoplait containers to hold my brushes and as water containers. You'll want at least two water containers: one to swish you brush in to clean it as you change colors, and another with clean water to thin the paint. I put a small drop of liquid soap in each so the water flows better, (soap softens the water). My LED light has a magnifier in it, but I also use some high magnification reading glasses (like +300) more than anything. If my painting can pass the reading glass test, it'll look good to the naked eye. You'll need an ex-acto knife and blades. And a rag or two. The rag is made of cotton and I use it to dry my brushes, and to help blend paint with when I do "dry-brushing." And a couple of sheets of paper towels, to dry brushes with, because they do it faster. You'll want to mount the figure to something so your hands aren't touching it, and wash your figure with warm water and soap before you prime it. Oh, you'll want a primer to paint the whole figure with first so the paint will adhere to it better. I like white or a light gray primer, just make sure it's made for figures, again because it has small pigments that won't hide detail, and don't be afraid to prime the figure twice. It may go on heavy but it will thin as it dries. I also like to have a small cardboard box that has a paper town taped to it to use to help hold my hand steady as I try to paint fine detail. You'll want something to paint on. I use a 12" x12" piece of flat floor tile, and a white plastic tupper-wear type container top as my pallet. I'll drip a few drops of paint onto this, maybe a drop of water to thin it, or keep it from drying out, and use it to blend colors on.
Ok, this is enough for now.
In closing, first, thanks for asking. You can buy starter painting kits on Amazon, and they're probably cheaper than if you bought them in a hobby store. I know Vallejo makes a starter kit, and a kit for federal soldiers too, so you can get started with a basic setup for maybe $100.00 which would include a few fine brushes (from Hobby Lobby or Michaels), some paint and primer, and you'd be good to go. I'd start out with the basic colors and learn how to use a color wheel for blending two colors. I have over 100 different paints and washes, because I'm lazy and don't want to blend, but also I'll paint for a few days and then not touch the figure for a week or more. I don't want to try and remember how I got that shade of blue, (did I add 3 or 4 drops of ivory to the Prussian blue?).
As I said earlier, I'm self taught, and maybe that's a good thing. I've got my own way of painting and my own style. It's not better or worse than anyone else's, but it's mine. Someday I'd like to think that some of my figures will be handed down to my grandchilderen.