Do it right!
If you're trying to learn the wet-on-wet (also known as "alla prima") oil painting technique popularized by Bob Ross on PBS's "The Joy of Painting," you need to understand that Bob does things a very specific way, with very specific tools, and a lot of advice that people or salesmen will give you will go directly against his recommendations or practices. Bob is not your average painter. His method is fast and "lazy." (His words, not mine.) Most of his tools are more expensive, but I've tried doing it the cheap way with entry-level stuff only to get frustrated and upgrade to his tools so I could make more progress.
Amazon has a "Bob Ross master painter kit" for like 60-70 bucks. If you want to start on the right foot, start with that. Don't go to the store and just buy the basic "art student" kit. It won't work, and you'll just get frustrated! Bob's kit has most of what you need. There are a few other items that you'll need, including easel, paint cleaning system, a color palette, and of course a canvas.
Why the tools and supplies matter:
Bob employs a wet-on-wet technique which means he covers the canvas with a base layer of liquid/magic white or gesso before doing the actual painting. That allows you to mix the color on the canvas instead of doing all the mixing on the palette. You paint fast while the canvas is still wet. As such, he recommends that people NOT use canvas boards since they dry faster than canvases. If the canvas is dry, his technique doesn't work. He also prefers pre-stretched double-primed canvas. Again - more expensive than cheap starter canvas, but when you do Bob's mountains, if the canvas stretches when you push, they fall apart. It needs to be taut.
The tools you'll need:
Brushes
You will need a 2" and 1" brush with organic or natural bristles. Synthetic bristles do not work. Trust me, I tried. Don't waste your money. You also need a fan brush with the same kind of bristles, and a palette knife. A small script liner brush is really optional. He mostly uses it for twigs and signatures. He also uses a round brush occasionally but I haven't needed it yet and I've done more than a dozen of his paintings.
Liquid or "Magic" White
You need a can of liquid white. You can make your own using linseed oil and titanium white but it's hard to get the mixture right. I bought a bottle of his trademark version and I found that to be much easier than trying to make my own.
Brush Cleaning System
You need a can of odorless paint thinner. Bob always says "make sure you check if it's actually odorless before you leave the store." His kit doesn't include this. Art stores have a jar meant for this kind of thing. It has a wire rack in it to break up the paint on the bristles. You fill the jar with odorless paint thinner, and scrub the brush against the rack. Then you beat the brush against the lip of the jar to get it mostly dry. Then you use a paper towel to complete the drying. Put the jar in a trash can or cardboard box so you don't spray flecks of paint everywhere when beat-drying. Don't buy a ton of thinner. It lasts forever pretty much, and it's not easy to dispose of.
Easel
You'll need an easel. I got a 20 dollar tabletop version at the art store and it's fine though it does slide some. His standup model is pretty costly. If I'm still painting a year from now I'll upgrade.
Paints
You need to use Bob's paints. Or, at least very stiff oil paints. They're waaaaaay more expensive than what you can find at a big art store. But the thin stuff turns you into what he calls a "mud mixer." Thin, cheap paint does not work with his technique. As an example of just how thick his paint is, he sometimes takes his palette knife and sticks it on a dab of titanium white and then lets the knife hang. Cheap paint will just let the palette knife slide right off. For the list of colors, just watch the show and see his list at the beginning. People keep trying to convince me to use acrylics. Bob doesn't use acrylics. He uses oil. Occasionally, he uses gesso for his base layer but that's it. Everything else is really stiff oil.
Palette
Lastly, you need a palette. Go cheap on this if you want. It's just a plastic sheet where you mix paint. Nothing fancy.