A quick correction: don't worry about finding something "cheap" right from the start, because actually entry-level kits often cost way less than you'd think. The thing is, it's more about picking the right type of model based on what you like to look at or use. A car to assemble is generally more doable for a beginner than a plane - fewer fragile parts, fewer technical adjustments after.
Check out classic brands like Tamiya or Revell: they have car models that are really designed for beginners, with clear instructions and pieces that fit together nicely. Tamiya especially has a whole "beginner" range where you only need glue and basic paint. If you want something even simpler, there are no-glue assembly models too, but honestly they're a bit less satisfying in the long run.
Before you decide, ask yourself: do you just want to assemble and display, or would you like your model to actually run/fly after? That completely changes the price and complexity. And since you mentioned "like a car or plane," do you have a preference between the two, or are you really open to anything?