Depending on who your local supplier is (and where you are located), a general description will not do you a whole lot of good. If you don't mind a little shipping costs, I would recommend using our gracious host for this forum...foosball.com. They have a variety of different style balls to choose from, and a knowledgable staff to help you make a selection.
If I where to make a recommendation, it would be to get a urethane ball, something with a little grip. I could give you the durometer specification, and all of the jargon, but that will not do a whole lot of good.
You hear us throw out name brands, and specifically with balls, because they each have different characteristics. And since there are so many to choose from, other than the very hard, or very soft foosball, everything else is hard to quantify with words, so we just call them by the name of the manufacturer. Sometimes with other short descriptions because the manufacturer may have a couple different styles of ball.
In your case, I would recommend a Shelti or Dynamo or Warrior type ball. Grippy but not to soft, made of urethane, and stays round! Those are good foosballs to start with. The Tornado ball is also urethane, but a little harder, so a little less controlable, especially on your table.
You also asked about what size to look for. That would depend on the size of the serving hole (if present) in your table, and what kind of ball return there is. I know that they have measurements for each of the balls that they sell at Foosball.com, so they can certainly be of help.
If you go to your local retailer, unless they have the "name brand" balls, the ones they sell will probably just be lightweight, very slick, white, generic foosballs that offer no control, and you will not be able to build your foosball skills very well with them. But that is just my opinion...of course.
Let me know if you need some more information.
Pat Ryan