I'm designing a 4 layer PCB and I know that the standard stack-up is

Signals
GND
VCC
Signals

(GND and VCC can be switched depending on the layer with more signals)
The problem is, I don't really want to connect all ground pins through vias, there are just too many of them. Maybe because I'm not used to 4 layer PCBs, anyway, I've read a tip by Henry W. Ott about a different stack-up

GND
Signals
Signals
GND

(Where the power is being routed with wide traces on the signal planes.)
According to him, this is the best stack-up possible with a four-layer PCB, for the following reasons:

Signal layers are adjacent to ground planes.
Signal layers are tightly coupled (close) to their adjacent planes.
The ground planes can act as shields for the inner signal layers. (I think this requires stitching.)
Multiple ground planes lower the ground (reference plane) impedance of the board and reduce the common-mode radiation. (I don't really understand this one.)

One problem is cross-talk, but I really don't have any signals in the third layer, so I don't think that cross-talk will be an issue with this stack-up. Am I correct in my assumption?
Note: The highest frequency is 48MHz and  there's a WiFi module on the board, too.

You will hate yourself if you do stack up number two ;)  Maybe that's harsh but it's a going to be a PITA reworking a board with all internal signals.  Don't be afraid of vias either.
Let's address some of your questions:

1.Signal layers are adjacent to ground planes.

Stop thinking about ground planes, and think more about reference planes.  A signal running over a reference plane, whose voltage happens to be at VCC will still return over that reference plane.   So the argument that somehow having your signal run over GND and not VCC is better is basically invalid.

2.Signal layers are tightly coupled (close) to their adjacent planes.

See number one I think the misunderstanding about only GND planes offering a return path leads to this misconception.  What you want to do is keep your signals close to their reference planes, and at a constant correct impedance.

3.The ground planes can act as shields for the inner signal layers. (I think this requires stitching ??)

Yeah you could try to make a cage like this I guess, for your board you'll get better results keeping your trace to plane height as low as possible.

4.Multiple ground planes lower the ground (reference plane) impedance of the board and reduce the common-mode radiation. (don't really understand this one)

I think you've taken this to mean the more gnd planes I have the better, which is not really the case.   This sounds like a broken rule of thumb to me.
My recommendation for your board based only on what you've told me is to do the following:

Signal Layer
(thin maybe 4-5mil FR4)
GND
(main FR-4 thickness, maybe 52 mil more or less depending on your final thickness)
VCC
(thin maybe 4-5mil FR4)
Signal Layer

Make sure you decouple properly.
Then if you really want to get into this go to amazon and buy either Dr. Johnson's High Speed Digital Design: A Handbook of Black Magic, or maybe Eric Bogatin's Signal and Power Integrity - Simplified.  Read it love, live it :)   Their websites have great information as well.
Good luck!
