Let me guess... erm Quake 2 by any chance... :rolleyes:
No flies on you, eh.
Like it or not, the main draw of the NatAmi is SuperAGA (that's what sets it apart from the FPGAArcade). Reading through posts on natami.net, the impression I get is that the graphics side of the chipset is where most of the improvements are being made at the moment. To help sell the NatAmi it makes sense to showcase the area where it offers the biggest improvement over the competition, do we at least agree on that?
From what I remember of your previous posts, you didn't/don't use your Amigas much for gaming. Nothing wrong with that, we're all free to use our computers how we wish, but I do wonder whether part of your assertion that I have a 'teenage boy racer mentality' comes out of this.
My concern is with showing NatAmi off, to generate more interest. It doesn't have to be competing with cutting edge devices, but it does have to be interesting, and when I say interesting I mean in a 'I never expected a retro machine to be able to do that' kind of way.
Your suggestions were a web browser and a paint program. Amigas already had great paint programs, plus to make the most impact you'd have to find talented artists to produce work using it, and that art needs to be noticeably better than the great work already produced on Amigas. How do you intend to make that difference noticeable? More colours?
As for the web browser suggestion, let's say we're looking at a faster, native port of Netsurf, which is probably the best option. Take a look at this screenshot of the native RiscOS version, and tell me honestly, are you interested in buying the machine it runs on?:

Don't get me wrong, a web browser is definitely going to be a useful tool in getting people to buy, but it doesn't push the machine to the limit in a way that's truly going to grab people's attention. It's an essential, not something special.
With the estimated price a NatAmi is going to cost how many folk who are really willing to pay that price are going to do so just to play a 3D style game that they could do so better on a higher powered and cheaper PC or games console...
The idea is not that they'll buy a NatAmi to play an old game, but rather that it'll inspire them, knowing how much power they've got their hands on, to do great things with the machine. Think about when you first saw what the Amiga could do, the focus wasn't on mundane applications like spreadsheet and word processing software, it was on the power of the machine; the graphics, the sound, the fast multitasking, etc...
Believe it or not, I'm not tied to one game, and I'm trying to encourage some creative ideas, but they have to meet the criteria, and the only criteria is that the software must push what the machine can do in a noticeably impressive way. Think about if NatAmi got some magazine coverage, what would you want the screenshots to show?