To provide a bit more detail, I made use primarily of GURPS 4e, Psionics, Tactical Shooting, High-Tech and Ultra Tech. I also took a little from Biotech.
I developed my own research tree, where the players allocated points to available options. As per the traditional X-Com game, some projects were dependent on autopsies, interrogations and captured equipment.
I had to make lasers more effective than they were in default GURPS, where they use fairly grounded (and thus conservative) assumptions. Most of the rest of the tech was aligned with GURPS defaults. I had good fun building out the various sets of advanced armour, as well as the story-oriented research reports.
I had the players manage the overall X-Com research system as a meta-task.
Instead of managing the overall X-Com budget, the PCs were instead responsible for their own team's budget, and could order weapons, amour, medical tech, ammunition, etc based on what they were able to produce or buy off the general arms market. They were also able to invest in intensive training courses, as per the GURPS training rules.
Although the PCs nominally reported to more senior officers, they were given extensive authority to make their own calls while in the field. One of the conceits of the campaign was that the PCs were selected specifically because of their inherent resistance to alien psionic influence, which made their decisions far more trustworthy than those of most people.