The cheapest option would be to give it a go with your 18-55 since you already own it. After that, the faster (in terms of f/stops) the better and wider gives you longer exposure times before you see trailing. Personally, I much prefer manual focus lenses for astro. Samyang give really good performance for the price. However, they are limited for other uses because of the lack of auto focus and auto aperture. I think you'd be best to look at what lenses you want for other photographic interests and just factor in the astro side. For example, the nifty-fifty isn't a bad lens for astro and is generally considered a must-have by the normal photo folks. Add a set of tubes and you have a macro lens. It's also cheap.
You'll read it over and over - Invest in a mount. That might be a commercial eq mount or a homebuilt barndoor. Either will make a big difference.