What would be the best lens for shooting long distances and lens for street photography on a budget?

For street photography I use one of my Canon "pancake " lenses. Either the 40mm f/2.8 STM or 24mm f/2.8 STM. They are reasonably priced, small, light and very unobtrusive but produce stunning image quality.

For wildlife I use either my Canon EF 70-300 IS f/4-5.6 or my Sigma 150-600 f/4.5-6.3. Not cheap lenses and the Sigma is a big heavy beast but I am very happy with the results from both.

The more mm on the lens, the nearer a distant subject will appear to you. The cheapest would be a 500mm mirror lens but beware, optical quality is very low.

Street photography varies a lot. Those who go for detail shots would do better with a short telephoto (~40mm APS-C). Those who want to see most of the street action do best with a wide angle lens (~20mm APS-C). Most would be comfortable with a low normal/standard lens (28mm?).

What lens did you get with the camera?

Any lens will shoot long distances, just the subject will be very, very small if it's not a telephoto lens. What do you mean by long distances? Stars in the night sky? Wildlife? Sports? As examples..... You can take star photos with a kit lens, and a tripod. Wildlife, maybe with a 55-250 or 70-300 lens, it depends on where the wildlife is and how big it is. Sports.... can be trickier depending on the sport and whether it's indoor or outdoor and how much light there is (the same as for wildlife to some extent).

Street photography on a budget could be done with a 50mm f1.8 lens which is about the cheapest lens you can buy, but you'd be limited on subject matter because of the crop factor. or the 40mm f2.8 STM lens that is a little more expensive. Ideally you'd want a 35mm lens that on a crop sensor gives a 50mm focal length that is about the same as what the eye sees.

To be honest, assuming you got a kit lens (18-55), I'd work with what you've got and learn all the basics (like what focal length gives what field of view) then you will be better placed to make a judgement on what you need, or would like to get. Photography on a budget can be very limiting so it would be better not to spend money for the sake of it.