In a few of my own places I've painted stairs, it's a pretty easy DIY and can really transform the look. I've painted a few solid white, meaning I've painted both the riser and tread in white. I've painted some with a black tread and white riser. The colour choice really depends on the house and the look you want to achieve. The above image is my house with white stairs. I've also painted another set of stairs in the house in solid white (behind the chair in this image below). I've used a floor and porch paint on the stairs, and in the past have always used oil but I know it's been discontinued so I'm not sure about the level of durability of the latex floor paint.
If you prefer the look of a black tread and white riser this is also a pretty simple painting project. But it does involve more prep time, you'll want to tape the sides of the black tread so you don't get black paint on the white riser. It also is a good idea to let everything dry well before you move on to the second colour. Here is the black and white example, I think it's a nice classic look.
Another aspect to consider is adding a runner to the stairs. This adds another level of decor and gives you a ton of options for adding colour and pattern.
This is a picture I've had in my inspiration file for years, love how this runner looks on the solid white stairs.
If you're adding a runner it's important to consider the amount of stair you want to cover, I prefer a wide runner, leaving just an inch or two exposed on either side of the runner (I find the one above is a bit narrow). You can also add nice details like the metal bar between each stair.