I think what some of the older guys are talking about (And you know who you are) is "etching" your own PCB versus sending off the Gerber plots to a fab house and having a PCB done. Not many of us do that anymore, as having a PCB fabbed is pretty cheap compared to all the muss and fuss of having all those chemicals and having to cut the raw copper clad board IMHO.
Anyway, what I like to do on my PCBs is use the top and bottom layers as VCC and Ground reflowed polygons once the board is 100% routed. (I use Protel98, I'm just learning Eagle.)
That does 2 things:
1) you get some intergral capacitance on the VCC-Ground polygons, which you want for decoupling(Use .1uF around your chips anyway) purposes, and 2) it tends to balance out your copper across the whole board. If the copper is not balanced across the whole board, if you should ever want to do something like wave reflow of your board, the heat will curl your board up like a potato chip if the copper is heaver in one area. The temperature expansion coefficient of copper is much different that of the PCB material like FR4. It's more important the bigger your board gets.
Just try to be aware of isoloated islands if your using the polygons as connections to your power connector. Keep it in mind as you do your routing.
So after all that, to answer your question: Having a "ground Plane" on both the top and bottom won't hurt anything for your application, but it WILL make it harder to modify if you need to change it someday.