Is it your computer that is slow or your broadband?
If the computer is slow ONLY when you are using the internet (web pages take a long time to load) then it is probably your broadband that is slow.
So you could have the fastest computer in the world but if your broadband is slow the pages will still take a long time to load.
To answer your specific questions, the 1.5ghz refers to the speed the CPU works at, so in most cases the higher the number the faster the CPU.
I have a desktop PC and the CPU on mine runs at 3.3ghz so quite a bit faster. So a 1.5ghz CPU is quite slow.
Note that laptops and notebooks often have slow CPUs in them to use less battery life (the faster the CPU the more battery it uses).
However the speed of the CPU is only one factor in the performance of a computer and it can be influenced by a number of other components (hard disk, graphics card etc).
In terms of RAM 1GB is very small and probably not really enough to run Windows 7, it needs about 3Gb or 4Gb as a minimum. Again the more RAM you have the faster the PC will go, though once you go above a certain amount of RAM it wont go any faster.
If you use your laptop connected to the mains most of the time then buy one with the fastest CPU you can, also a "good" graphics card will show video better.
Generally you get what you pay for.