Back in the days when a Pentium 4 and 512MB of RAM were common it was harder for cheaper systems to browse the web. These days it almost doesn't matter at all which CPU you get for web browsing. The main thing you want to look for is a dual core CPU and 4GB of RAM minimum. Computers at my college still use old Pentium D's from the year 2006 and honestly I do not notice much if any slow down at all when browsing the web on them. Pretty much any dual core CPU will do simple web browsing with ease. No need to worry about an Intel Core i3 being slow for that purpose. That said, you still want to get the best for your money. Don't get a core i3 when you can get something better for the same price or only slightly more. Shop smart today and tomorrow you will thank yourself.
Look more for laptops that will give you a better experience when using them. A laptop with a nice keyboard is something that can truly be taken for granted. Also, go for an LED backlit screen. LED backlit screens are much brighter than the old screens and use less power at the same time. Consider the screen size as well and the touchpad. Good battery life is also something you should look for. Get a good brand too like Asus or HP. I have personally had excellent experiences with both brands and they have excellent customer service. HP especially has great customer service.