Crikey, that's a lot of upgrading. Personally I would advise against doing them all on the same day - it will make troubleshooting any issues much harder, as it will be more difficult to ascertain which upgrade caused the problems.
Personally, I would upgrade in the reverse order that you listed, i.e.
Windows 2000 --> 2003
Domino R5.? --> R7.0.2
BES 4.0 --> 4.1.x
When I upgraded Domino 6.5.4 to 7.0.2, I left the Bes server (full version, not express, in case that makes any difference) in place, and had no problems. However, my BES was already 4.1 by then.
I have never upgraded Windows under Domino, so can't provide too much assistance there.
Domino, again, I usually keep fairly up-to-date and have never tried a R5 to R7 upgrade. I took R5 to R6 to R7. There are some upgrade issues from R5 to R6, so they will almost definitely be there with R5 to R7. Have a look at IBM Redbooks | Lotus Notes and Domino 7 Enterprise Upgrade Best Practices
Sorry, not too much solid advice in there, except... I really would not attempt upgrading all three in one day. There are some Domino processes that only run overnight (or as per the "out of hours" specifications on the server docs) and these really should have a chance at completing (so you can find or fix errors) before BES is changed.