The link includes a cake cutting chart, as well as serving sizes, and typical tiers that go together nicely.
Things to consider:
First of all 10,12,&14 is way more cake then needed. It will be crazy heavy and super expensive to make!
Also you need to make sure these pans will fit in your oven. A full sheet cake will not fit into a standard oven.
The picture is lovely, make sure you use proper supports, boards under each tier and a display board that is thick enough to carry the weight of all the tiers put together, you need internal supports as well (the larger the tier the thicker dowels and obviously more in the larger tiers-cut to the same height).
Are they serving or saving the top tier? If saving, a 10"round is a BIG cake to put in the freezer
If they're serving the top tier you could make one quarter sheet cake and make a 6,9,12" or a half sheet and 6,8,10-doing something like this will give you the opportunity to use these pans more often.
I would definitely do a trial run on your tiered cake, especially since you've only made one before-you don't have to make all three tiers but at least the smaller two so you can practice stacking, etc.
Work ahead: Day 1 Bake cakes. Day 2 Make buttercream or ganache, level, torte, fill and crumb coat, place cakes in fridge to settle. Day 3 Final coat of BC on cake, cover with fondant if doing so. Day 4 Stack cakes and add final decorations. It doesn't have to be exactly like this, just an idea of how to break up the work so you don't get stressed and can take your time.
Figure out how your going to transport all this cake, you can box each cake up separately and stack at the event, just make sure you have boxes and room beforehand. I always place nonskid lining on the floor of my car and underneath each cake board in the cakes boxes-the last part my fiance says is overkill but I'd rather be safe than sorry lol!
Good luck, very nice of you to make her cake as a gift.