We've got a few threads about miniature painting. My favorite is this
one, but I'm biased. Let's start with the basics.
What do you need? You need paint, brushes, and some miniatures. For paint, the most common brands among hobbyist here in the United States are going to be Citadel, Army Painter, and Vallejo. Any one of those paint brands is fine. As you gain more experience, you might find you like some colors in one brand more than you do in others, but just to start out with, these are fine. You should be able to find them in a nearby hobby shop or through an online vendor. I would maybe avoid Citadel because they're a bit on the pricy side. They're fine paints, but expensive for what you get. You might also find paints brands like AK Interactive, Two Thin Coats, or Pro Acryl in your area. Those paints are fine as well.
Do not go overboard on purchasing paint. i.e. Don't buy every single color out there. Start small with a limited palette of colors. Army Painter does sell some decent starter sets, so that might be a good place to start. But you could just buy a few colors you want to use with whatever miniature you have in mind to paint.
As far as brushes go, I don't have any specific recommendations for brand. Since you're just starting out, I'd go for the cheaper brushes first. You can hit up any store that sells art supplies, like Michael's (if you're in the US), where you can find inexpensive brushes in the sizes you want. I typically purchase a variety pack of smaller brushes and use them until they die. Brushes are going to be more expensive at your local hobby shop and I don't usually think it's worth the premium you pay.
When it comes to miniatures, get the ones you think it'd be fun to paint.
Reaper Miniatures has been my go to for fantasy miniatures for nearly thirty years. They have a wide variety of miniatures and you'll likely find one that's pretty close to whatever D&D character you happen to have. Do they make the best models? No. But when it comes to quality and price, I think they provide more value than most other producers. You might find their models at your local store but you'll definitely find them online.
WizKids is another company whose products you're likely to find at your local game store but you'll find them online as well. While these models are reasonably priced, I just don't care for most of them. I do like some of their monsters, like the Beholder, and their dragons, but for regular PC type miniatures I avoid them like the plague.
Citadel Miniatures (Games Workshop) are the gold standard for high production, quality models, but they are overpriced. I say that as someone with a fairly extensive Warhammer 40k collection. $40 for a single miniature is probably a bit much to ask a new person to spend. I'd avoid them for now unless you can find some used models for a good price.