I'm currently running Windows 7 Ultimate 64-bit, and I use the Aero themes with my performance settings set to "Adjust for best appearance". I have an AMD A6-3650 (all stock), and 8GB DDR3 1333MHz memory (dual-channel). No discrete graphics card. My question is, would switching to the Windows Classic interface and setting my performance settings to "Adjust for best performance" offer any speed benefits to my computer?
From a developer's perspective, no. When you use the DWM you take advantage of the composted desktop which means application windows don't have to repaint as much, which has certain performance benefits.
Under Windows XP many GDI/GDI+ operations are hardware accelerated, such as BitBlt, filling in shapes, drawing text, etc - however Windows Vista removed most acceleration, Windows 7 brought some acceleration back, but not as much as XP's had - however this setting is (I don't believe) controlled by the System control panel.
God developer/blogger Raymond Chen wrote a good article about this setting, actually, and how it's largely irrelevant today: http://blogs.msdn.com/b/oldnewthing/archive/2013/03/27/10405554.aspx
Because Windows Aero is actually an 'extension' of the classic layout that is in many ways drawn on after all the Classic desktop calculations are already processed in the background there are usually noticeable UI response benefits. At the very least, Explorer uses less memory, doesn't go to the GPU as often to render effects (which is faster than Aero simply because all the CPU related drawing tasks in classic would still be done in Aero in addition to those GPU tasks.) Whether someone can quantify exactly how much is a good question, but tests by crippling my 6 core 3930k show that classic mode is far more usable when I take out all the Ram cards and leave just 2GB of DDR for my system to use, or limit myself to a single core with all 8GB installed.
Whether those benefits noticeably extend outside of Explorer is unlikely, but really depends on whether your machine is under stress at the time you are testing this. Seeing as 99% of the time you use your system Explorer is running in some form, if you want to gain the very last drops of performance out of your system it would be a good idea to "adjust for best performance". I know most headless servers I have ever seen have this configuration, (and not just for RDP) as well as many Server 2008 machines in an intensive environment.