comparing CPU’s in Laptops

I am looking to buy a new laptop, but I don’t have too much of a budget. I have tried to find a site that explains the difference between processors, but I can’t find one that explains them in plain language. I did find a computer that had everything I wanted, but was told by a friend that the processor is old technology. It had a Celeron M 1.5GHz Processor. My question is:

1. Is this an adequate processor if all I am doing is basic typing and internet or should I be looking for a different processor?

2. What should I look for in a processor when comparing?

Thank you

Kyla