(not op but Moderately Addicted to the funny medieval skinnerbox)
On desktop, most of the playerbase uses RuneLite, since it's free and open source, has some nice quality of life features, supports user-created plugins, and has been explicitly allowed by Jagex. Just be careful to only download it from runelite(dot)net, as people sometimes make fake runelite websites to use as phishing scams and the like. There's also the official steam client and the default client, which aren't bad, it's just that RuneLite is quite good.
On mobile, afaik you're stuck with the official app, but tbf it's surprisingly good, especially for an mmorpg designed for desktop, ESPECIALLY one based on code from 2007.
(Also if you're new to osrs, the wiki is really in-depth!)
What program do you recommend for playing it?
save