All-season tires are what most folks are looking for. Of course, they aren't truly all-season, as they suffer when winter conditions show up: heavy snow, ice, slush, a lower temperatures. But for the rest of the year, they're ideal, and in warmer, drier climates, they've fine for year-round duty.
You can go the budget route with all-season tires, but a better bet is to choose a well-known manufacturer, such as Bridgestone, BFGoodrich, Goodyear, Michelin, Continental, or Dunlop.