I had universal tires on my car as a cost-cutting attempt - figured out pretty quickly that was a mistake. In a city full of potholes they're sluggish, they whine on the highway, and in summer they actually get softer. Then I switched to summer tires with reinforced sidewalls and forgot about the problem.
For a Sportage on bad roads, summer tires will be way better. The reinforced sidewall structure isn't marketing - it's a real solution: it keeps the shape when you hit a pothole or curb edge, which is critical in a city with torn-up asphalt. Plus summer tires perform more consistently in summer and last longer.
Look at mid-range and above brands - they make special lines for exactly this kind of situation. You don't need the top models, but the manufacturer's reputation matters. Read reviews specifically for your size on the Sportage, because one model can behave completely differently depending on what tire size you go with.