Also the P4 seems a lot more expensive than the celeron
The best way to consider a Celeron is as a cut-down version of the P4. If your Tiny is a few years old either processor is likely to look like a huge improvement but if you compare a P4 and Celeron of the same speed, the P4 will run almost all programs faster. In the long run the P4 is probably the better buy.
The motherboard appears to have an on-board graphics adaptor but it looks as if it's pretty rudimentary so, unless your Tiny has a separate graphics card, you'll probably need one of these too. FWIW, all Tinys I've ever seen had on-board graphics.
Again, if your old computer is a few years old you'll probably need new memory too.
If the old one is not P4 based you'll almost certainly need a new power supply.
But the good news, floppy, DVD, hard disk, keyboard and mouse should be easily transferable to your new machine.
I would also recommend E-buyer - they have good prices, are reliable when it comes to delivery and are pretty good at returns if you have any problems.
Despite the odd comment from others, I'd wish you good luck in upgrading your computer - everyone who does it starts from your position. With a bit of help you should find that it's not too daunting!