Very good points.
Rubes, congrats on your purchase. I went through the same dilemma with my ride. Here's what works for me, after significant investment on tyres and rims 3 times over to get the right fit.
1. Always use original rims with correct hubsize for e38. Offset should be no more than 25, preferable between 20 - 22
2. When moving from 16" to 18", ensure you keep spec of radius and tyre size. I would recommend the use of 235/50/18 Michelin Primacy LC, the best tyres I have ever used on the 38. Super quiet, supergrippen and supercomfy!! Otherwsie, the next alternative is 245/45/18. I would never use anything lesser than a 40 series on the 38, as in my experience that will severely impact ride comfort, suspension, bushes and lower arms
3. If you choose a staggered option, pls do not go more than 10JJ. You will have serious problems finding a tyre and will be a very costly affair. Staggered set up is super awesome and I love it on my 38
4. As AB mentioned, the moment you go low profile, you will compromise suspension handling. I would recommend if you go down this route, then a proper suspension set up is required to balance compromise on handling. If you choose a Titan set up, you can use your ori springs. If you choose other set ups, I am not so familiar. avoid using a sport/lowering spring on standard shocks. it will again compromise your ride
I find this site very useful as a tyre guide for the 38
http://www.meeknet.co.uk/E31/Timms_bmw_wheel_and_tyre_page.htm