The "hand" option is really more of a technique to set exposure - take a picture of your hand and use it to set WB and you will quickly see that it is not really a viable option most of the time. Do yourself a favor and pick up a gray card - even if you start with a simple cardboard one from your local camera shop, it is better than nothing. The idea is to place the card in the spot where you intend to shoot, trying to position the card so there is no glare reflecting off of the card into the camera lens. Take a picture of the card, filling the majority of the frame with the card and properly exposed (you can check the histogram on the display of your camera to check this). Once you are satisfied with your image, you can use this image of the gray card to give the camera the data it needs to set the WB off of this image. If your lighting conditions change, you will need to shoot another gray card image. If you do not know how to do this... read the manual that came with your camera to see if it possible and how to do it. I know it sounds cliche, but you can learn a lot from the manual!
The camera's preset WB settings are okay, but often times if there is more complex light, the presets will not be able to accommodate that condition and will introduce casts, etc. Shooting RAW, among other things, permits you to set the WB after the fact, once you have downloaded your images to the computer - then you can go to town with the WB eyedropper, etc. However, you can always make this adjustment on any image within Photoshop, etc. using the gray eyedropper (in the Curves and Levels adjustments). The idea is not to select something that is bright white, because that will often be overexposed and lack meaningful data - you want to select something that is light gray - neutral and not blown out. So, if you can find something in an image that you think is pretty neutral, you can use it to balance your image. Using a gray card, either before the shot or included in the actual shot, will give you a known reference to click on. Once that WB is set (beforehand) or clicked on (in post processing) you can typically apply that WB correction to all of the images shot under similar conditions (i.e., "batch" process the WB adjustment for the whole set of images at once). Of course, you can always adjust the "corrected" version to suit your artistic preference or your memory of the image as you perceived it when you shot it (i.e., clicking on the grout in the tile in your original image may have given the "correct" WB, but I thought it would look nicer to warm the image a little to give more pleasing, although not necessarily "accurate" skin tones in the face). Sometimes you are concentrating so much on taking the picture instead of making the image and you don't have the time to take a picture of a gray card or twiddle a dial or change a menu setting - that's where knowing how to tweak things in post becomes important. You always want to try to make the best image possible in the camera, but, speaking for myself, that is a proposition I am constantly trying to achieve but have not yet consistently attained. In an ideal world, post-processing would be to make your great images look stellar, but for the rest of us, we need all the tricks we can get.
As far as cloning goes - just practice with a soft-edged brush and learn to adjust the size of your brush as you clone - in Photoshop this is done with the left (increase) and right (decrease) square bracket keys (e.g., [and] ). It pays to develop the habit of cloning onto a new layer so that you leave the original image undisturbed. That is, make a new layer directly above the layer you intend to clone in, make that new layer active, then do you cloning on that layer. You will have much more flexibility in the edit if you do it this way. Cloning can be simple or very time-consuming and arduous depending on what you are trying to accomplish.
Have fun and practice on this image - this image contains a lot of fun things to challenge your developing skills (WB, contrast/curves and cloning) so have at it and se what you get.
Good luck - have fun!
Kirk