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I will qualify my comments by stating that I own a 2004 (AP2) S2000 with 36.5K miles on it. There are AP1 (MY00-03) vehicles out there that may meet your mileage requirement as well. The AP1's will rev to 9200-9300 RPM and the AP2's will rev to 8200-8300 RPM, depending on where the rev limiter is set. This translates to some pretty high piston speeds in a 2.0-2.2L I4 NA engine. If you find one that is FI, then I would say synthetics are definitely the way to go for maximum protection.
With that being said, I'd have to say the S2000 is very easy on oil. I don't think I've ever seen a bad UOA, even when 0W20 was used by mistake during a Las Vegas summer. Even RP 10W30 seems to work well. But the most popular oil is probably 10W30 Mobil 1. The best UOA's I've ever seen were on a MY03 using AMSOIL TSO, ASL and ATM. But the owner was using an AMSOIL dual bypass oil filter system, so I'm not sure how much that skewed his flawless UOA's.
There are two issues that you will most likely be concerned about if you buy an AP1 (the less civilized of the two generations). Oil consumption is very common and high. You may find that some oils consume less than others. Also, installing Krank vents have helped many with this issue. The other concern, even though the engine is pretty bullet proof, are cracked valve retainers. This is caused by a mechanical over-rev (mis-shift at high RPM's). Have the valves inspected by a highly qualified tech ASAP after buying your AP1. You might as well have the valves adjusted too while he's in there.
The AP2 does not consume any oil as a rule, but there are a few that use a little bit. The only quirk that I have noticed is that some oils quiet valvetrain noise better than others.
I don't have any experience with the OLM, but previous Honda recommendations don't seem too dangerous to me. They said to use 10W30 or 5W40 for 3750 or 7500 mile OCI's prior to the OLM. I personally split the difference to 5K mile OCI's.
Since you don't have your S2000 yet (and I know you can't wait), it's difficult to recommend a specific oil for you to try. But if it were me, and I didn't have a significant oil stash already, AMSOIL 10W30 ATM would go in there first.
Be careful and get used to your new S2000 before you decide you're ready for the racetrack. It's a wonderful little car!