First off, I would definately find out from the landlord if it is ok for ya to have kitty. Is there a pet deposit required, etc. Then, I woulmd consider if the 2.5 year old is ready for a kitty. Usually parents will get a kitty for small children and then when kitty scratches child, back to the shelter kitty goes. Make sure to teach child to be careful with kitty; gentle and all that.
Ask the shelter employee for her name and number incase something should come up. Ask to see kitties vet records, if any, or ask for the name and number of the vet she was taken to for shots and check up. Ask if Kitty has been around small children before. Ask how well kitty gets along with other kitties or doggies; no one knows what the future may hold. Ask what kind of food she has been eating, changing foods on her, especially in a stressfull situation like adoption and new home could cause diarreah. Ask what the return policy is for the shelter. If things don't work out, will they take kitty back. You may not get your money back, but think of it as a donation to the shelter.

Always remember if you need advice, Holla at Pet Talk!!!! That is why we are here!!!
Good Luck!!!
P.S. Ask if she is aggressive. Some places may or maynot tell ya, but ask anyway and make sure to get the name and number of the shelter worker who wil be meeting you.