Your best bet for a long flight time will be a powered glider, with a flight profile of using the prop to get to altitude, and then gliding until you start to get low again. I've flown my Calypso glider for 20 to 30 minutes on a 1300 mAh 3S battery. Gliders also tend to be good for learning, as they tend to fly more stable and sedate, giving a new pilot time to react.
The Calypso was discontinued some time ago, but there are numerous powered glider models available on the market. Whether you'll find anything in the price range you stated, however, is another matter. All too often, cheap RC airplanes reveal shortly after buying them, why they were so cheap to buy in the first place. What you might consider is looking for a flying club near you, and seeing if anyone there might have a used setup they no longer use, that they would be willing to sell. If so, you stand a better chance of getting a decent plane without breaking your budget.