This is for my old laptop, which is currently running a 2.6ghz Celeron, 512MB ram and native graphics, Ubuntu 7.1 gnome

Which is the best browser for this particular build?

So far I've tried

Opera latest beta
Firefox latest beta
Swiftfox

Cannot really decide as I notice some webpages load quicker than others depending on what browser you use. Also - I was only able to get Flash to work for Firefox/Swiftfox, and it seems a lot choppier than on my windows box even after letting a movie load the entire way.

Any advice about those 3 or perhaps something I have not tried yet? Thanks!

I use iceweasel, have you tried it yet? Its not the greatest but it does everything I need it to.

No, he hasn't tried Iceweasel nor is there any reason for him to do so. There are actually two things called "Iceweasel" out there, and the one you're familiar with is actually Firefox for all intents and purposes. Due to a conflict between Mozilla's branding and Debian's Social Contract, Debian wasn't able to use the official Firefox label. As a result, Debian created a "fork" of Firefox which is completely Firefox compatable--the only differences are removing references to the Firefox trademark and logo.

This problem is unique to Debian, due to the specifics of Debian's Social Contract. Every other Linux distribution either has no problem with Mozilla's restrictions or has made special exceptions to accomidate Mozilla. That's okay, because most Linux distributions are lead by "men" rather than "laws". Debian is the only Linux distribution which fundamentally lacks a "benevolent dictator" who can make exceptions to the "laws".

I use Opera and have used Opera on lower spec boxes than that and been happy with that; alternatives are firefox and konqueror (konqueror's use of fonts is a bit odd at times, which makes rendering look odd at times, but otherwise its an under appreciated browser; I quite like firefox, but not half as much as Opera - handling of tabs and bookmarks is, imho, not as good as Opera).

What I would point out is that there a whole list of reasons a browser could be slow apart from the browser itself.

Name serving could be slow, and you probably should use dig to check that out. (I believe browsers vary in how often they get tghe name service to refresh, and I think mostly this isn't end-user-adjustable, so I suspect you are stuck with what the browser thinks is best.)

So you could consider caching look ups, if that is a problem.

There is also browser caching, which is end user adjustable and there may be mileage in that. And you might chose an external cache (squid, polipo). The problem here is that if you devote too much memory for caching, that will mean the computer doesn't have enough memory for the other stuff it has to do, and that will eventually lead to swapping and that will slow down the computer. (I once had a computer with a bit of a problem and it actually seemed to run its broadband connection slower than dial up with exactly this sort of issue.)

So you want something lightweight ?
Try:
kazehakase
dillo

I personally use FF no matter what. The ads are just impossible without adblock, noscript, and the like.

I've found that third version of FireFox works much faster than opera 9.2 / opera 9.5 / firefox 2 for me, and it IS more stable than FF2 with all the same extensions, even in its betas.
I've been using it for about two-three months now at home and work, I've used opera 9.5 (with search-in-page-from-address-bar turned off, 'cause it lags greatly) at work / 9.2 at home before that, FF2 before 9.5 betas.