I did some analysis on how to get the techs best.
Here's a pic of the SCI civs (without Russia):
Order of donation
Assuming it is three independent blocks, it seems best to me to alternate between these blocks of civs that seem to know each other.
I'd start gifting up Sumeria (most backward), then Korea, then Greece.
Then (if necessary) Ottomen, Germans, Babs, Persia.
When to buy
I think best buy is when one of each group got his free tech. While it's cheaper for us if two got the same, it still has good value to all other civs.
Get even
We should stop as soon as we got all three 1st tier techs. Sell Medicine or Steam to get back our gpt (not Nationalism if possible).
Watch out
IIRC Baby, Ottomen and Persia have been in the race for Sistines' for some time (
see Andro's comment). Though the window to finish Sistines' is just three turns wide, we should try to not let them get ToG. If one of them finishes it, most likely a cascade would rob us Newton's the very next turn as it's 200 shields cheaper...
However getting the 4th free tech has higher priority imo.
edit:
In sum, the advantage of war with the Russians is that the Babs will give us full price. The disadvantage is that we can't get the Russian free tech. As the first civs we bring into the new age will be the backward ones, not Russia and Babylon, I conclude that there is no reason for war.

Good conclusion. Anyway we should still be able to dow Russia if we find out that Babs are the only civ to get Steam while all others have Medicine and we got no chance to buy Steam...
