First off, Vallejo's idea of red oxide primer is a set of 6 paints, allowing for shadows, highlights, mid-tones, "volumes", (isn't that something women do to their hair?) and whatever else they deemed necessary;
Funny, they only show 5 color swatches here...The fourth one looks close to being the base coat, so go with something like that if you don't want to shell out for the whole set.
The green-grey you want would be Vallejo 972 (107) light green blue. This seems to be the overall choice from various opinions to be a good representation of RAL 7009 green-grey. (Sorry, no 6 paint color system here). It also appears to match preserved equipment in this color that I have personally seen.
Elfenbein... "ivory"...let's go with Vallejo 918 (005).... Ivory.
And of course, black.
Now you get to figure out which color goes where and with what time period of construction. I lifted this general description from David Byrden's article on panzer colors as a rough guide;
"In the lower interior of the tank, the grey-green covered just about everything. Transmission boxes and other modules, which were perhaps manufactured separately, were ordered to be delivered in grey-green. Torsion bars, levers, transmission shafts, floor panels (yes, top AND bottom surfaces) storage boxes, etc. were painted uniformly grey-green.
In late 1942, the manufacturers were ordered to stop using the grey-green paint, and leave the bottom of the tank in its original red primer. Wherever grey-green had been used, red would appear instead. This was definitely a step backwards in terms of ergonomics - the red paint was quite dark. However, Mr. Doyle has found plenty of surviving vehicles proving that this order was obeyed. Sometimes he finds a red lower area with a grey-green transmission box or turret motor, because such items were stockpiled for some time before use.
Within the upper, Ivory part of the interior, all items of what I would call "working machinery" were painted black. This includes MG mounts, movable handles, vision ports, gearboxes and handwheels, etc. Also, it seems that every equipment stowage point was labelled, by hand or later with decals. In both cases the writing was black and had no background."
You are going to need photos to help you in your process, Google is your friend, unless you want to start throwing money down for some books. And I wouldn't use the restored (or even the unrestored) Bovington Tiger as your Bible either...The blue-green they used during restoration is so very wrong. There are other problems as well, like the green breech on the unrestored vehicle.
I know you realize this kit is not exactly state of the art by any standard (cough, cough) and the interior leaves much to be desired. Here is some discussion about other's efforts to bring her up to....well...some kind of standard;
http://www.network54.com/Forum/47207/thread/1244489324/Tamiya+1-25th+Tiger+I+turret+and+hull+corrections-
Good luck!