I tried a York Schmidt wrap a few days ago, good for learning the mid-high range, but the low end was shot, the rotors were tough, and the perinet valve was a touch wobbly. With 800-1200 worth of work, it would be worth giving as a starting horn. It was 800. I doubt you'll find anything I'd recommend for less than 1000. And, I get guff from folks, but I don't think one should start on just an F horn. For the past 100 years these should be considered specialty horns meant for playing period correct classical repertoire. Even if it is a small kid, get them a compensating horn if weight is a concern.
You never know what you can find on E-bay. A couple years ago, I purchased a Reynolds Bb single on Ebay for $200. I originally thought it would just be a clunker that my grandkids could honk around on before their first year of band. But.... turns out, it's such a nice instrument, I've actually used it in performance. Also because it's so nice, I won't let my grandkids touch it until they are mature enough to handle it carefully when they start grade school band. It's going to be both a wonderful "starter horn" and an instrument one of them can use through high school if desired.
All of our french horns come with a mouthpiece and case and are guaranteed playable. Please take a moment for check out our website and feel free to call us (ask for Erik) with any questions ph#(303)458-5900
please remember that every used horn purchased from a garage sale, eBay, or Craigslist almost always have intonation tubes that don't slide and valves that are sticky. Every used french horn we've ever had into our shop had these same issues. Repair shops typical charge $75 to $150 (and up) to rebuild the valves and "un-stick" the intonation tubes.