ok I think u want a web traffic stat system cause what u described are things that traffic stat scripts do. now if you want one of those and want the number to show on the page,then i dont know, but i suggest you use bravenet. they do everything u descibed and and you can have visits counts or reg counts, its a hosted counter but its worth it

i use it on my site, you can make up to 3 for free. but if u want more, you can always make additional accts.