Mora or other Scaninavian-style knife is a good choice. Perhaps look for a "youth" or "Scout" models that have guards; a #39 has guards, wood handle, and leather sheath for under $25. For a tighter budget the #601 has guards, painted wood handle, and a plastic sheath for $13. Mora is probably the least expensive, but other brands are in your price range too. As mentioned, Marttiini is a big higher quality but still in the $25 range for a wood handle Lynx model. Helle quality is excellent, and the basic models are still in your price range.
AG Russell Woodswalker is about $20 with a leather pocket sheath. Nice little set for the money.
Not sure the current prices, but the Buck Woodsman and Pathfinder are very durable and come with secure leather sheaths.
Good luck deciding!