In Apocalypse scientific research by X-COM falls into two specialized categories, Biochemistry and Quantum Physics. Essentially what this means is that it will be necessary to have 2 different streams of scientists and laboratories.
The original base will contain 5 Biochemistry and 5 Quantum Physics scientists, together with a Biochemistry Lab and a Quantum Physics Lab . Each scientist has a skill level that can vary from 60 to 100 skill and can be assigned to any lab that they specialise in.
Each research facility can be assigned to any project available. It is possible to transfer research projects over laboratories at different bases but it is not possible for 2 laboratories to work on the same project at the same time. When a laboratory has a project assigned it the total value of the scientists skill assigned to it will contribute towards reaching its total 'research cost' every hours.
Research cost is the "skill hours" required to complete a project. If a laboratory has 5 scientists assigned, with a total of 400 skill hours per hour, that means that a research topic that takes 8000 will likely be complete in 20 hours when you put 5 scientists to work on it (20*5*80=8000).
The Technology Race
Research should initially be focused into developing the advanced Biochemistry Lab and Quantum Physics labs in order to allow research on more complicated topics, and double the number of personnel that can be assigned to them.
Biochemistry research will benefit X-COM in tactical fighting (due to Biological Warfare and later Alien Gas). When the focus moves onto attacking the aliens in their home dimension, it will allow research on weaknesses of each alien building.
Quantum Physics will produce results regarding new technologies that will benefit both Cityscape Fighting and Battlescape combat. It will eventually generate new ships that will allow X-COM to cross into the alien dimension.
As X-COM captures alien artefacts it will be a key priority to research them in order to be able to upgrade its vehicles and agents weapons and equipment. This is due to the aliens levels of conflict escalation, through which they will increase their destructive abilities and threaten to outgun X-COM. The rate at which the aliens will update their technology is in direct response to X-COM's overall performance.
It will also be necessary to deploy upgraded workshops to be able to produce the sufficient number of craft, weapons and equipment necessary to re-equip X-COM's forces as the technology race continues.
X-COM will win the technology race by being able to keep pace with the increases on alien abilities in order to defeat them.