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Java Swings GUI, changing the display based on which button is clicked. What is the ideal way to implement this?

I'm pretty new to programming Java based GUI applications. Here's what I have in mind, I want to divide the window into two areas.
The first are contains buttons (or a list), and based on which button was clicked, or which item was selected, the second area changes. (finite number of buttons)
Something like this:
I can think of many ways to do this, but I am not sure what is the best practice. Do I have several invisible panels and make only 1 panel visible at a time, or do I change the ordering (bring panel x to front), or is there some other way?
Appreciate any help I receive!! Thanks in advance!

Although this is a primarily opinion-based answer I'd go with a Nested Layout approach:
Main panel with BorderLayout. Or you can use the frame's content pane which already has BorderLayout as default layout manager.
Left panel with BoxLayout (or GridBagLayout).
Right panel with CardLayout.
Note: Buttons in the left panel should switch right panels cards.
See Lesson: Layoing Out Components within a Container tutorial.
For complex GUIs you have also third-party layout managers available, listed in this answer:
MiG Layout
DesignGridLayout
FormLayout

Make buttons unresizable

So I was trying to google how to set a default size to JButtons so that they don't grow as the JFrame is resized. I didn't see a setDefaultSize method but the closest one I could find that does a similar job is setMaximumSize(). However, it doesn't seem to work in my situation and I'm guessing it's because I'm using Grid Layout for positioning my buttons in the frame, here's a small piece of my code:
rightPanel.add(ButtonA);
rightPanel.add(ButtonB);
rightPanel.add(ButtonC);
outerPanel.add(leftPanel);
outerPanel.add(rightPanel);
getContentPane().add(outerPanel);
Here's a picture of what happens:
I would also like to have my buttons in the middle of the right panel when I'm resizing (just like they are now but a lot smaller). Any idea of how I can fix this? I'm assuming that I have to use another layout or something.
Thanks
EDIT: I modified my code to use BoxLayout but it does not seem to put the buttons in the middle. The X Alignment is working but Y Alignment is not doing anything:
ButtonA.setAlignmentX(CENTER_ALIGNMENT);
ButtonA.setAlignmentY(CENTER_ALIGNMENT);
ButtonB.setAlignmentX(CENTER_ALIGNMENT);
ButtonB.setAlignmentY(CENTER_ALIGNMENT);
ButtonC.setAlignmentX(CENTER_ALIGNMENT);
ButtonC.setAlignmentY(CENTER_ALIGNMENT);
JPanel rightPanel = new JPanel();
rightPanel.setLayout(new BoxLayout(rightPanel, BoxLayout.Y_AXIS));
rightPanel.add(ButtonA);
rightPanel.add(ButtonB);
rightPanel.add(ButtonC);
outerPanel.add(leftPanel);
outerPanel.add(rightPanel);
getContentPane().add(outerPanel);
EDIT2: Fixed with vertical glue.

A GridLayout will always resize the components to fill the space available.
Try using a vertical BoxLayoutinstead. See the section from the Swing tutorial on How to Use Box Layout for more information and examples.

Encapsulate each JButton in a JPanel with a FlowLayout, and then add those FlowLayout JPanels to the rightPanel instead of the JButtons themselves. This will allow you to keep your evenly spaced buttons, but won't make them expand to take up the entire space that the parent container has available.
If you don't want them evenly spaced, but to be three consecutive buttons one after another top down, you can make the right panel have a BorderLayout, add a sub panel to the north area of the BorderLayout with the original GridLayout that the right panel had, and then add those FlowLayout panels containing the JButtons.

Choosing the layout managers and number of panels for Java GUI

I would appreciate, If anyone here is kind enough to recommend me what are the layout managers to choose
and how to separate the attached GUI into Jpanels.
Thanks so much in advance.
What I have tried so far:
Jframe - BorderLayout
Map (the grid and clear button from another class extending jpanel) - so I have put it in jframe.CENTER
the buttons to the right: jframe.EAST
I put them in a jpanel in a gridlayout (but I cannot get the spacing between the components)
buttons at the bottom: jframe.SOUTH
I put them in a jpanel in a gridlayout (but I cannot get the spacing between the components)

When trying to determine what layout(s) you should use, you should start by trying to determine areas of responsibility...
For example...
Based on your needs, I might start with a GridBagLayout. This might seem complex, but if you break the UI down into seperate components, focusing on their individual needs, it should become simpler...
For the panel on the left...
I would be temptered to use a GridBagLayout, simply because it allows the components to use there preferred sizes, but still allows you to set up a grid like pattern...
For the arrow buttons...
This becomes a little more complicated, but I would use a GridLayout(2, 3) (2 rows, 3 columns). This will require to add a filler panel at the first and third position along the top row, but still maintain the buttons at a equal size...
For this panel...
I would be tempted to either use a GridBagLayout, because it will allow you to span the rows or even split it again into two separate panels, with the controls on the left in a GridLayout(2, 1) and the control on the right in something like a BorderLayout as required...
For "progress" panel...
I would be tempted to use...GridBagLayout. Mostly because it would allow you to provide more weight to the progress bars then the labels.
For the main panel...
I would probably be tempted to either use a BorderLayout, with the Clear Map on another panel of it's own, allowing it maintain it's preferred size, in the NORTH position and the map panel in the CENTER or even a GridBagLayout depending on what the invidual components are...

Cosmetics with GridLayout

I'm posting this question because I'm new to programming at the present time and I have a pet peeve that when I create the app I don't want the objects to go across the entire window.
I use GridLayout the most often and I was wondering if there was a way to make components such as a JTextField or JTextArea NOT span the entire window, leave a little space on both ends?

You can add a component to a JPanel, which uses a FlowLayout by default and all components are displayed at their preferred sizes. Then add the panel to the layout using the GridLayout. The panel will increase in size but the components on the panel will stay at their preferred size.

Help with setting up panels in Java

I'm new to Java awt, so I am having trouble with setting up panels. I have one giant panel, which needs to hold 3 panels inside (photo is attached at the bottom). One will go on top(1), second one will be in the middle(3), and third goes on the bottom(2). Any remaining space has to be divided equally between (1)/(3) and (3)/(2). Also, the middle panel (3) is a table, so GridLayout has to be used.
How can I achieve this?
Thanks in advance!
P.S. I've tried to draw it in MS Paint (http://i45.tinypic.com/mwejkk.jpg)

I don't understand all, I suggest :
Use swing, not awt, so use JPanel
A BorderLayout, with your giant panel (jpanel) in middle, a jpanel at west ; for this jpanel
a BorderLayout, or BoxLayout, or GridLayout and put inside your 1 2 3 panels.
... or use netbeans and matisse.

This will help you a lot. It's a Sun tutorial on BoxLayout. It describes the stacked layout that you appear to need, and also how to make invisible components to add gaps in the extra space you mentioned. For the middle pannel, put a GridLayout in that panel to do the things you need.