If you use an *air-dry* clay --like PlayDoh, Crayola Air Dry Clay, etc., or a homemade version like salt dough or bread clay-- you won't be able to harden the finished items completely before the party is over. Air-dry clays usually take overnight to harden reasonably well (depending on thickness of course), though their drying can be speeded up some on a low-temp oven and/or in front of a fan in a non-cold, non-humid room. (Purchased Play Doh in particular will usually crack though if the drying is speeded up.)
If you give the kids something stiff to carry their items in on the way home though, that should work well enough (perhaps a paper or plastic dish or box) to protect them on the trip then allow to dry at home.
Be aware though that all air-dry clays will have a problem with later humidity or bugs though if they're not also *sealed* (which needs to be done after drying). That could involve painting over the whole object with acrylic paints, or applying a coat of water-based sealer like polyurethane, Future floor polish, permanent white glue like Elmers GlueAll thinned down about 3-4 to 1 with water--or ModPodge which is the same thing, etc, on top of the dried clay.)
You may be thinking of *polymer* clays though which ARE baked in the oven for a short time to harden them....in fact, they need to be heated to harden since they are oil-based and will never "dry."
You could certainly use polymer clay for the sculpts and bake them (15-30 minutes for most things) so they're be completely ready to take home.
I don't know what kinds of sculpts you have in mind for them to make (and don't know who "Spenser" is), but that could make a difference in which brands (and lines) of polymer clay would be best.
The cheapest polymer clay would be a 2 lb box of original "Sculpey" which comes in white or terracotta colors. That particular clay is *very* soft but any parts of the things made with it which are thin or projecting out will break off after hardening if stressed very much. SuperSculpey-flesh (in a 1 lb box) or 2 oz packages of Sculpey III are better, but still not as strong in thin areas after baking as the brands/lines called Premo, Kato Polyclay, Cernit, or FimoClassic, and FimoSoft would be in-between. For my kids classes, I usually used Premo as a good middle-of-the-road strong clay unless the kids weren't making anything with thin parts, but I'm not all that familiar with the newer FimoSoft. Most polymer clays need some kind of "conditioning" though to make them completely smooth and pliable, and the stronger clays will usually need more of that.
Another thing to consider re "breakage" would be joined parts falling off. When raw clay arms/legs/heads or other bits are added to other raw clay parts, there needs to be a good join or the parts can get knocked off after curing. That usually just means pressing a reasonably large area of each piece to the other piece (which sometimes isn't easily understood by kids), or things like a small-length-of-toothpick,etc can be used as an armature inside the clay joining the pieces, etc.
(And btw, polymer clays don't require any sealing, but can be given a coat of gloss finish if desired, or even painted over--usually with acrylics, 2 coats or 1 coat of gesso plus one coat of color.)
IF you are interested in polymer clay, you might want to check out at least a few of the pages at my polymer clay "encyclopedia" site that deal with baking the clay, simple things that kids can do with polymer clay, etc:
http://glassattic.com/polymer/baking.htm
http://glassattic.com/polymer/Conditioning.htm (if needed)
http://glassattic.com/polymer/kids_beginners.htm
and because Halloween is getting close:
http://glassattic.com/polymer/Halloween_etc.htm
HTH, and have fun!
Diane B.