Kolchak was the most open Monarchist. Denikin was a Monarchist, but he didn't want the old order to return, and could probably settle for a Republic. Another factor would be the Duma. How influential would the Duma and the civilian politicians be allowed to become. The Socialist Revolutionaries would probably be the largest party, and could the generals really stomach working together with leftists?
Considering the Ukraine, it probably depend on Poland a lot. One can assume the Polish like OTL expanded their border eastwards due to the relative instability in Russia. A Ukrainian state could probably only be created as a Polish puppet (or as a warlord state under some White general nominally loyal to Petrograd). Ukrainian nationalism was strongest in East Galizia, but I can't see the Poles not annexing that region.
Woul Petrograd or Moscow be the capital? I guess it depend on where the leaders feel more comfortable to rule.
Turkestan: Well Bukhara and Khiva both declared independence OTL, so their survival would depend on Russia's ability to wage a Central Asian campaign. The Kazakh territories are more problematic. I could see the Alash Orda party try to establish some kind of autonomous region within Russia (but raise a militia ready to revolt if the Russians become too unpleasant).
The Caucasus: The Democratic Republic of Armenia, the Democratic Republic of Georgia, the Azeri Democratic Republic and the Mountainous Republic of the Northern Caucasus would probably be declared as OTL. Again their survival would depend on Russia's ability to reconquer them. The Kuban and Don Cossacks also declared their own republics, but with a White victory they'd probably try to aim for some kind of autonomy within Russia.