Well, it's a good thing you haven't bought anything yet, so you can be spared the suffering. Do NOT, I repeat, DO NOT under any circumstances buy an HP/Compaq desktop computer! They combine shoddy parts with shoddy workmanship to make -- you guessed it -- shoddy systems. Unless you're interested in a system that crashes all the time and waiting a few hours listening to Muskrat Love the Musak version while on hold with tech support, just to talk to someone with an Indian accent so thick you can't understand them and has a set of canned answers for every question, don't buy HP/Compaq.
Now, to answer your question. Put simply, the Celeron is a CPU you should never buy. Intel took an inefficient design in the Pentium4, and then removed all the features of the chip which help mask that fact. The AthlonXP, made by rival company AMD, cannot be beat in a bang per buck comparison. It can often run circles around a P4 clocked 400MHz faster. Save a few select applications, the AthlonXP is the CPU to get for budget minded people who don't want to give up a lot of performance.
I am planning to purchase a new processor (HP or Compaq) and notice there are Athlon XP's and Intel Celeron Processors. What is the difference and preferably better processor to purchase?