Sarah, those three speed hubs are pretty indestructible, and most bikes like that haven't been ridden anywhere enough to wear them out. So even if the cable isn't adjusted right, it's probably not a big deal. Tires are going to set you back $30-$35 for the pair of tires, tubes, and rim strips. Easy to install. You'll need a pump. Make sure they are 26 x 1 3/8 and not 'Schwinn' tires. You want them marked 37 x 590, not 37 x 597.

Give us good in-focus photo or two of the right side of the bike, showing the state of the gear cable, and we'll talk about what the gears need.