There's little risk of harming most stones with whatever's chosen to lubricate it. Most of the difference in use will come down to some lubricants doing a better job of suspending the swarf, making the stone less prone to clogging. Some 'wetting' agents used on a stone won't suspend swarf at all, or they'll do it poorly, allowing more swarf to settle deeply into the stone's pores. But clogging can be remedied with a little elbow grease & scrubbing and/or lapping (resurfacing) of the stone. So, it wouldn't be 'ruined', per se.
I would suggest, with a 'cheap' stone, using a decent oil that does a better job suspending the swarf will help to keep the stone working as effectively as it's capable. That's an unknown with a cheap stone, however. Some very cheap ones can't be helped much, no matter what's used on them. Cheaper stones will usually glaze faster and they may not shed grit efficiently enough, meaning the abrasive at the surface will become worn and lose it's cutting effectiveness. And if the lubricant isn't preventing clogging as well, the stone will become slow and almost completely ineffective very quickly.
A few types of waterstones, specifically, are bound with a material that, if used with the wrong wetting agent, could effectively ruin the way the stone works. These stones are made to release grit in a controlled & predictable manner when used ONLY with water. Using oil or something else can foul that up and completely change how (or IF) the stone continues to release grit and expose fresh cutting grit. But such stones usually come with strict warnings about the risks of using something other than what's recommended for them.
In general terms, it's very hard to beat mineral oil for use on designated 'oil stones'. Most stones bought at the hardware store will be of this type, a 'Coarse/Fine' double-sided stone in two shades of grey (light/dark), usually in aluminum oxide. Simple mineral oil is cheap & readily available in most places, and it does a very good job keeping swarf suspended on the stone. You can see this in how much black stuff can be wiped from the surface as you work. Use a microfiber towel for that. If the lubricant isn't suspending the swarf well, you'll notice there's not much black stuff being wiped off (because it's already settled deep into the stone).
