M.J.
Some stuff is trial & error, like Nancy W. said, you'll find that you buy or are given some things that you never use & there will be others that you can't live without. I don't know what your budget is like, but here are the things that I use on a daily basis which can be found between Kohl's, Target & Wal-Mart/Sam's Club:
Coffee pot w/ permanent filter
Wolfgang Puck knife set -- whatever brand you like, but get something decent or they won't stay sharp for long
Cuisinart hard anodized cookware set -- you can certainly get a cheaper set that will last several years, we've been on our own for 16 years & just got this set 2 Christmas's ago
Collander
Oster Fusion blender/food processer -- has pre-programmed buttons for smoothies & food processing plus crushes ice with no problems
Wooden cutting boards for fruits/veggies
Plastic cutting boards for meats
Measuring spoons & cups (dry & wet)
Wooden spoons
Rubber spatulas
Pot holders
Set of mixing bowls, either plastic or glass
Cookie sheets
Roasting pan
Glass bakeware (2 & 4qt covered, 9x13 & 7x11 oblong)
I would get 8 place settings of dishes as well as silverware so if you have guests over you'll have plenty for everyone
2 sets of sheets per bed
2-3 towels per person