Why is it one or the other?
Personally, I'm an atheist, and I believe in evolution... However, one can believe in a creationist force, and still believe in evolution... Isn't it a bit naive to think that a creator wouldn't tinker with his creation? Of course, from the Christian standpoint, the creator is a perfect being, and would have created things that didn't need tweaking, but meh...
But anyways, the two concepts are not mutually exclusive (though again, personally, I don't believe in any higher powers, so my evolution is an unguided one)
Why do I believe in evolution? It can be witnessed happening in real-time, that's why...
It is an observed fact that life forms can change from generation to generation... Reproduction is a fairly complex system, and things go wrong all the time... Perfect copies are rarely ever made... Offspring will almost invariably have some odd change from their parents' blueprints...
How have we observed these sorts of changes? We see them in rapidly reproducing life forms such as bacteria and fruit flies... It has been witnessed happening... This is completely incontrovertable... It is absolute truth... Species do change over time...
At this point, though, people usually begin screaming "but that's microevolution, not macroevolution!" and "You can make small changes to something, but it can never turn into something else!"
To that, I give the following analogy:
Take a gallon of red paint... Add a drop of blue paint... Yes, it makes a change (micro), but it's not enough to really talk about, right? Add another drop... Still not very noticeable... Keep doing this... What happens down the line? You get purple (macro)... But wait! We started with red! And now we have purple? And all we did all along was make tiny, barely noticeable adjustments? That can't be! That doesn't happen in living organisms! Oh, but it can, and it does...
There's no reason not to believe that if micro[/]evolution occurs, that eventually, it won't add up to macroevolution, and as I've already said, microevolution is an observable occurance... You can't say that it doesn't happen...
Why don't we have a good record of our lineage (or virtually any other species' lineage)? My guess is simply that we've only begun to scratch the surface (pun intended) of the fossils available in the Earth... We don't have all of the blanks filled in (or, really, any of them) because we just haven't found those "missing links" yet... Hell, fossilization itself is a relatively rare occurance (lots of conditions must line up for it to happen)... Don't be fooled by the seemingly large number of fossils we've found... It doesn't really happen very often when compared to the numbers of creatures who have roamed the planet, and the number of years they have been doing so... It's simply a fact that the fossils we do have have been created over a VAST number of years, over a VAST number of generations of creatures... Probability handed us a decent number of "jackpots" only because the pool of chances is so huge...
As for the age of the Earth, when countless people have found evidence to support something, and countless efforts to prove otherwise have failed, why not believe it? The scientific process is one of constantly attacking the "known"... Anything that withstands this battery is something that should be trusted (though the question must always remain, of course, so further assaults can be made upon it) Methods like carbon dating and such might have flaws... They might be entirely incorrect, but don't other methods exist? Haven't there been plenty of people who doubted the validity of C14 measurements, and have found alternatives? i'm sure there have... And I'm sure that most of them came up with strikingly similar results...
Also, 6000 years is NOT long enough for two people to become 6 billion... Look up population growth for actual estimates... Most charts say that 6000 years ago, the human population of planet Earth had to be somewhere in the millions... And heck, toss in the bottleneck of Noah, and you've got even worse problems... If 6000 years isn't enough time (and again, it simply, plainly, and irrefutably isn't) then choking things off even shorter is even more impossible...