the first number is the width of the tire in millimeters. 225mm.
so if you look at a tire and it says 245/40/18, then you know it is wider than a 225/40/18.
depending on the width of your wheel, there would be corresponding appropriate tires for it. on a 7.5" wheel, you can go for a slightly narrower tire, 215/45/18 or the right sized tire, 225/40/18.
the second number, 40 or 45, is the aspect ratio. it is 45% of the 1st number, and that is how thick or thin your tires would be. a thicker tire will be more comfortable, a thinner tire just looks a lot better.
the last number is the size of the wheel you are running.
to be able to calculate the best match for tires/wheels, people use a tire calculator.
http://www.rims-n-tires.com/rt_specs.jsp
for all season tires, you can get a lot of choices and cheap prices too.
like i mentioned above, try toyo proxes 4 or falken ziex912. also, dunlop direzza101, yokohama avid h4s, general exclaim uhp.