Seconding the clippers! And someone willing to do the clipping. (I do my housemate's claw-clipping; she holds the cat and distracts her with petting, I do the snippage and it only takes a minute. Thank goodness for good-natured cats! ...And it's a good idea to get the cat used to being held and having its feet handled by doing so at every chance.)

Scratching places are also very good to have -- especially a tall one, since they like to stretch aaaallllll the way out to scratch. :D

Other good things to have on hand might be a cotton balls and a gentle ear cleaning liquid (some cats get built-up waxy gunk in their ears that needs swabbing out, plus it's a good way to keep an eye on the ears for ear mites -- if the gunk is reddish-black, it's mites).

A comb or brush, probably just a simple "slicker brush" since your front-runner is a shorthair, might be a good idea, too, in case she isn't one for self-grooming as much as she should be (or just as a bonding/petting thing!). You might also look into a collar and/or microchipping, if the shelter doesn't do that as part of the adoption process; a frighteningly small percentage of lost cats find home again, so with our own cats we've done everything we can to up the odds.