I'm no expert, but I would start with gutters, and grading. Make sure the grading around the perimeter of the house is good, (sloping away for the first 10' at least) and pipe the gutters away from the foundation. That may be enough to cure the problem. During a decent rain storm, an amazing amount of water flows off your roof.
On the flip side, if your area does have a high water table which makes it to your floor level during "wet" time of year or after heavy rain fall, you may need to take additional steps. In that case I would start by just installing a perforated sump pit and pump. Even without an attached permiter drain around your foundation, the pit may be enough especially if you have a decent layer of gravel under the basement floor. If/when the water table rises, it should travel laterally through the gravel to the pit where it can be pumped out (preferrably to storm sewer but at least a fair distance from house) before reaching floor level.
In my area (Northern NJ), most houses with basements have gutters. I bet if I didn't have them I'd be dealing with basement flooding myself. I would definitely start there.
Also, talk to your neighbors and see how their basements are during these condistions when you get water. See what systems, if any, they have in place.