Arguably, the most prolific rimfire at Appleseed events is the 10/22. The Takedown version is certainly adequate, and you can use it as-is, but you'll get more out of the experience and learn how to be a better rifle shooter with the use of a sling, and better sights are never a bad idea. As I mentioned, I did two upgrades to my wife's 10/22 Takedown to make it a better Liberty Training Rifle (LTR) for the event. I failed to mention that I also put in a modified bolt release as well to assist with returning to fire after a magazine change.So is there a better "stock" rifle to choose than a Ruger 10/22 Takedown?
My Appleseed gun is a 10/22 carbine with Nodak Spud sights, a modified bolt release and a web sling in a Hogue olive drab stock with sling swivel studs.
One of the 50th anniversary 10/22 models from Ruger has a full stock similar to the Ruger American rimfire bolt action guns, and it has an aperture sight with a section of picatinny rail. I don't know how easy or repeatable the sight is to adjust, but if it isn't too hard to adjust and the aperture isn't too large (they marketed it as a ghost ring sight), this gun might be pretty good out of the box for Appleseed.
A while back, Marlin released a version of their 795 as the 795 LTR, featuring a web sling and Tech-Sights. The only issues with these guns for an Appleseed are that the single stack box magazine protrudes from the underside of the stock which can make a comfortable and stable standing position more difficult, and that the magazine does not fall free when the release is pressed. If you can find this model, it'll almost surely be a cheaper, quite acceptable option versus the 10/22.
For a write-up about the Ruger 50th Anniversary gun and comparison to the Marlin 795 LTR, here is a post on the Appleseed discussion group.
http://appleseedinfo.org/smf/index.php?topic=43961.0
There are certainly plenty of other guns you could use, but these two would be at the top of my list.