A quick way to create a custom toolbar panel In Illustrator with your most used / favourite that you can quickly access. Go to the window menu and toolbars and select the new option. Give it a name and click OK. You can now fill it with your favorites.
You can now edit this panel by clicking the three dots and you will see the complete list of all the available icons to be able to drag to your new box. You can display it as a list or a gallery, personally I prefer the list. Drag from there into the box to place the item in the position you want. You can place it above, place it on (to become part of a group) or below. You can also select any of the items in the box and shift them around, moving them above or below or onto (and becoming part of a group - though when it is only a few entries I am not sure why you would want to group them).
You can also select an entry and drag from the box back into the edit area to delete it, though it should be noted as with the groups, the application sometimes refuses to delete an item (the type features seem to be a tricky one to remove during trial run through and tutorials).
You can create multiple new boxes via the window menu and toolbars and new but you can also use the manage option (accessible via the edit option as well). Select the generated box in the manage dialog and click the delete button.
You can have multiple boxes with different sets of things such as rectangles, circles, stars etc or perhaps all the symbol features etc, not sure if there is a limit to the number of boxes. Re-display them (if closed) by going to the window menu. Select an item and apply as you would from the standard toolbar.
You can also show (via the edit feature) color, gradient etc - all are available at the bottom of the edit box. Click to show and click to remove from the box.