So in reading the upgrade paths Pz3's upgrade in house to Panthers.
Do you recommend upgrading to a Pz3 so I can in house upgrade to a Panther later on...
or
Pz4 because Pz3's do not have the same punch as Pz4's into 1942.
It is a very interesting problem and it is good that you realized it early on as it is never too late to start thinking about these things. Now I hate to say, but the answere is not simple as it depends on your playing style and general strategy. Different players will give you different answere as well. Personally, I usually upgrade 2-3 of the obsolete light tanks to Pz.IV and the rest to Pz.III. As you wrote, if you have too few long gun Pz.IVs then you might have problems dealing with the hordes Soviet tanks in 1942-43 as the long gun Pz.III is not really superior to them, more like an even match at best. To some extent it can be compensated by having more StuG IIIGs and other self propelled ATs. But they are not as good in the offensive as the Pz.IV. And if you only have the two starting Pz.IVs and lose one or both of them before the Panthers arrive then there is a problem.
But there can be other considerations, for example in our last full multiplayer game Uhu upgraded more Pz.IVs than me, up to 4-5 or maybe even more, to have a better chance for an early victory in the east. (And he upgraded some of them even before the arrival of the long gun version, so these had to be taken back to Germany once again.) The long gun Pz.IV is superior to the Soviet tanks until early 1944, when the T-34/85 and the other heavies start to arrive. But it is a kind of a gamble as if victory is not achieved early enough then the player ends up having a number of somewhat obsolete Pz.IVs in 1944-45 and there will not be enough prestige for many Panther upgrades.
And then of course there is the choice of having only cheaper Pz.III upgrades and more AT guns, save more prestige and then spend it on having a number of Panthers when they become available. In this way the player can enjoy technical superiority from mid/late 1943, but may have problems before that and as a result may run out of time. Nevertheless, as said, with some extra StuG IIIs and good tactics it can also work.
And then there can be times when the actual strategic situation overrides all previous considerations, e.g. your tanks can be just too busy on the frontline to be taken back for an upgrade of your choice. But if you postpone the important upgrades they will be easy prey to the later enemy tanks.
Finally, timing is also important as usually the early versions of these new tanks are more expensive and they become cheaper with each later version to reflect the increased and simplified production which reduces the price of the individual vehicles. Additionally, the early types have lower max fuel reducing their range which simulates the initial reliablility problems. Units with low fuel have to stop more often for a turn for refueling limiting their tactical value which simulates that they breake down more often and they require regular repairs limiting their effectiveness. For example the first version of the Panther, the Panther D is more expensive and less reliable (has less maximum fuel) than the later versions. So it may not be a good idea to upgrade all existing Pz.IIIs to this type. Perhaps the best is to upgrade only one or two to have some much needed boost in the frontline with these and then wait a few turns with the rest for the better and cheaper Panther A. Or maybe completely ignore the Panther D and only upgrade tanks to the better Panther A and even later to the excellent Panther G.
To make things even more complicated, note that one Pz.II and one Pz.38 can also get a scripted upgrade to a Marder AT in 1942 for a small fee if they are transfered back to Kiel in Germany. There will be an in-game message about that. It may also be a good idea as the Marders are not dead ends, check the upgrade charts on this. I guess players will again give you different answere if it is worth it or not. Just do what you think is right.
or
Should I wait until I can upgrade to a Tiger and use it for Partisan duty in the West while I wait that longtime before Tiger's are available?
In this mod Tigers are very expensive, so Tiger upgrades are generally not recommended. Maybe just one, if prestige allows, and if really needed. Historically, a Tiger I cost much more than a Panther and it is reflected here.
However, in late 1942 a single Tiger I unit will appear in Germany as a "gift" to the player for free which then can be transfered where it is most needed. But this unit has low fuel / reliability issues like the early Panther types. Later it can be upgraded to a better version with more fuel though.
I think using German tanks for partisan duties is waste of resources. Maybe one or both of the two captured French tank units can be used as such as these cannot be upgraded to anything. Or the weak Italian one that starts in the Balkans. But these can also be used in the east as support tanks for a while.
I hope it helped and did not confuse you even more.
At the very minimum I would strongly suggest to read the "Changes" and "Hints" sections of the in game Library - these do not contain spoilers just essential information about the various changes from the base game. These changes were made either to increase the realism or to better suit the needs of such a large and long scenario. While watching the videos I noticed that you were puzzled by some modified game mechanics, most of which are explained in the in-game Library and I think knowing and understanding them are essential for a victory. 
