Actually, your current info about AMD vs Intel is a bit outdated, going back to before Core 2 Duos were released.
First of all, a dual-core processor is a "two-in-one" CPU, where there are two processing cores in one package. This provides two execution cores for extra speed and insane multitasking.
Not too long ago, most PC enthusiasts and gamers would prefer AMD over Intel because they are more powerful. Intel developed just by increasing their clock speeds over time, whereas AMD developed by utilizing new technologies to attract power-hungry PC builders. Intel is cheaper and "faster" in clock speed, which is why many poeple get a "good ol' Pentium 4". But AMD pretty much controlled the gaming crowd back then.
But then, something happened: Intel dished out their new Core 2 Duo, which is by far "the best" processor, arguably better than an AMD. If you are looking for processors, a Core 2 Duo should be on the top of your list of choices.
There are many reasons why people would discourage you from getting a Celeron. For starters, it's a Celeron! They are on an even lower level than a Pentium 4, and they are one of the lowest family of CPUs released by Intel. They are not dual-core, and dual-cores are the only CPUs that should be purchased nowadays. It's cheap and has a high clock speed, but that does not mean it's "good". The performance of a CPU cannot be determined from just looking at the speed of it, there are many other variables. For example, the Celeron is a bad choice because its models only have 256KB/512KB of L2 Cache.
So to sum up, if you go shopping for a processor around this time, it should be Dual-Core, and maybe a Core 2 Duo.
Hope I helped!