What is the perfect base layout?

I would recommend dedicated the entire right side of your base to laboratories and workshops, save for 1 or 2 rooms, which you will need for facilities that get no adjacency bonuses.

You will need to build 6 facilities that get no adjacency bonuses (Officer Training, Alien Containment, Foundry, Psionic Labs and 2 plot facilities which cannot later be removed or moved), and 2 square blocks of 4: 2 Satellite Uplink + 2 Satellite Nexus for a total of 16 satellites (which is exactly the number of satellites you need) + 2 Power Generator + Steam Generator + Elerium Generator to power the whole thing (a base with such a layout will produce 107 power and draw 102 power; you can replace the Thermo Generator with an Elerium generator if no steam block is in a suitable location, allowing you to drop 1 Power Generator and placing one of the non-adjacent facilities there, freeing up a slot in the right wing for another lab/workshop).

As you can see, 6 + 2 * 4 = 14, the number of rooms in one side of your base + 2. The 2 extra facilities will overflow into the right corner of the base, as so:

You can shuffle the blocks around, what's important is that you don't put facilities that get no adjacency bonuses in such a place that it will block bonuses for facilities that do

Should you ever become rich like Scrooge, you can remove 1 Power and 1 Thermo Generators and build a second Elerium Generator, allowing you to move 1 facility that get no adjacency bonuses from the right side to the left side.

Note that the laboratories have been replaced with workshops - by this point you will likely have researched everything there is to research. You may also wish to demolish Alien Containment after interrogating every type of enemy, as doing so will turn surplus live aliens into useful corpses, allowing you to stun aliens for their enemies without sacrificing the body count, as well as free up a slot for a facility that doesn't have adjacency bonuses.

Proof of concept screenshot. Note my improper placement of plot facility 2 - it should be in a corner. Also note how blocks have been shuffled around to accommodate various demands over the base's lifetime.

Enemy Within addendum

The expansion introduces some new factors, but the situation remains largely unchanged: The Genetics Lab counts as a laboratory and the Cybernetics Lab counts as a workshop for adjacency bonuses, so you can build them as you would build laboratories and workshops above (make sure to fit the Gene lab in a corner if you're going to replace the laboratories with workshops later). The foundry has also been given workshop adjacency bonuses, so you can move it out of the laboratory block to the workshop block for some increased efficiency.

First things first: The number and location of steam vents and pre-excavated spaces will be random each game, and the optimal building strategy will depend on that, to a degree. If you can reach a large area of already excavated spaces by extending the lift down, this can save you valuable time and credits early on. If the only steam vent is next to your satellite uplink, you should forget about it, etc.

If you want to make full use of the adjacency bonuses provided by the new Genetics Lab and Cybernetics Lab facilities, you will have to prioritize between them, the Officer Training School, Foundry and Alien Containment as you won't have the space to build all of these facilities early on, while leaving enough room to make full use of the adjacency bonuses. There is no one right answer here, as it depends on how you want to approach the combat layer.

There are four types of adjacency bonuses, in descending importance: Additional satellite capacity from Satellite Uplinks and Nexuses build next to each other, Money and resource refunds from Workshops, the Foundry and the Cybernetics Lab, increased research speed from Laboratories and the Genetics Lab, and extra power from the three Generator facilities.

Uplink adjacency is absolutely essential, to the degree that you need to designate a 2x2 grid on the left side of your base for them. In order to not lock yourself out of Abduction missions completely, you should leave two countries on your starting continent without satellite coverage. If you don't lose any countries, the best way to provide nearly full coverage (14) is with three Uplinks and one Nexus. If you lose two or more countries, you can cover the remaining ones with four Uplinks.

The refund bonus from Workshops et al. is not essential, but very helpful. If you want to build more than one satellite in the first month, you usually have to construct a Workshop on the right side of the access lift for the additional engineers. With Enemy Within, you can now construct either the Cybernetics Lab or the Foundry in the next space, providing you with your first refund bonus, while leaving room to expand downward for a 2x2 or 2x3 grid. Since the refund bonus has been increased (from 7% to 10%) in EW, you could max it out with a 2x4 grid, but you're well beyond necessity at that point.

Research takes longer in EW, which makes the research bonus from Lab adjacency more helpful, but it is still possible to skip Labs entirely if you make a priority of fully covering South America with satellites and capturing aliens for the research credit. Eventually, weapon fragments will become the research bottle-neck, as usual. However, as you will want the Genetics Lab anyway, building one or two Laboratories next to it won't go to waste. You can do this in the far left or far right columns, extending the adjacency downward. If you wanted to construct a 2x2 grid, you either would have to wait until you excavate the bottom two levels, or delay constructing Workshops on the right side of the base, neither of which I recommended. Once you have researched everything, you can safely remove any Laboratories you have built, but you should be able to finish the game at will at this point.

Unless you get lucky with your steam vent placement, you will have to build quite a few regular Power Generators as you expand your base. I tend to build three or four on the right side of the base, and maybe some more on the third level beneath the Satellite Uplink, depending on how early I can get an Elerium Generator. The Adjacency bonus is quite necessary as regular generators don't produce much power on their own. A well-placed steam vent can save you a lot of time here. Once your first Elerium Generator is in place, you can start replacing the Power Generators with Workshops or other facilities.

It is possible to make do with only two Elerium Generators for your final base if you're frugal: only build one Laboratory, and remove the Alien Containment before you build the Gollop Chamber, once you've interrogated all aliens.

Below is a sample base layout, at 91/92 power:

+------------+------------+------------+------------+------------+------------+------------+
| O.T. School| S. Uplink  | S. Uplink  |    Lift    |  Workshop  |  Workshop  |Hyperwave D.|
+------------+------------+------------+------------+------------+------------+------------+
| Alien Cont.| S. Nexus   | S. Uplink  |    Lift    |  Foundry   |  Cyber Lab | Laboratory |
+------------+------------+------------+------------+------------+------------+------------+
|  Psi Lab   |Elerium Gen.|Elerium Gen.|    Lift    |  Workshop  |  Workshop  |  Gene Lab  |
+------------+------------+------------+------------+------------+------------+------------+
|            |            |            |    Lift    |  Workshop  |  Workshop  |            |
+------------+------------+------------+------------+------------+------------+------------+

And just for kicks, this is the really minimalist version, at 80/80 power:

+------------+------------+------------+------------+------------+------------+------------+
| O.T. School| S. Uplink  | S. Uplink  |    Lift    |  Workshop  |  Workshop  |  Workshop  |
+------------+------------+------------+------------+------------+------------+------------+
| Alien Cont.| S. Nexus   | S. Uplink  |    Lift    |  Foundry   |  Cyber Lab |  Workshop  |
+------------+------------+------------+------------+------------+------------+------------+
|  Psi Lab   |Thermal Gen.|Elerium Gen.|    Lift    |  Gene Lab  |Hyperwave D.|            |
+------------+------------+------------+------------+------------+------------+------------+
|            |            |            |            |            |            |            |
+------------+------------+------------+------------+------------+------------+------------+