There are number of selection tools are available in Photoshop, I get confused most of the time which one should I use and when? Is there rule available on this?

The hotkey for the arrow is V, which is referred to as the 'Move Tool'. I don't even know what the 'Artboard Tool' is, but it's not relevant.

The move tool does what it says. If you want to move something around, select which layer the thing is on, then select the move tool, then click and hold the object on the artboard, which allows you to drag it around. If you make a selection with marquee tool, then select the move tool, then click and hold inside the marquee selection, which allows you to drag it around. To unselect the marquee shape, click ctrl+D or go up to Select > Deselect. If you want to resize something, click ctrl+T, then hit enter when you're done resizing.

Just be conscientious of which layer(s) you have select and make sure you click V before you start dragging.

This post was edited by ericswanson_19 on Nov 30 2015 08:13am

If you need to make a precise selection, use the pen tool, it creates a path but you can convert it to a selection by right clicking after you finish it and selecting "create selection"
If you just need a rough selection, any of the other tools will do (lasso, quick select, magic wand, etc)
The polygonal lasso tool would be better for things that have straight lines and no curves, and the pen tool is anything especially if you need to make curves
You can select colors specifically if you use Color Range, under the Select drop down menu at the top
Also there is a "Refine Selection" option (not sure it it's only on newer versions) that you can use to refine a rough selection (basically readjust how much you want shown, whether you wanna smooth/feather/contrast the edges, etc)
And as said above, you can cancel selections by using CTRL+D, you can add/subtract to and from selections (if using a marquee/select tool) by holding SHIFT/ALT, and you can save and load selections if you need them for later
To save a section, after you make it, go to Selection and choose "save selection", it'll create a new channel in your document (next to layers tab) and to load selections, using CTRL+click on any layer icon will automatically select everything in the layer (same with channels)

Pretty much this, just play around with them and eventually it'll just come naturally what you should use in a certain scenario.