If you tile the long wall first, then bring the end walls close to the long wall, the caulk seam will not show as much as if you do it the other way. That way, you can tuck the long wall's pieces in, and not have a large void if you just bring them close at the corner. It also means any cuts you might need to make will have half of them hidden by the end walls edges. If you want to avoid caulk in the corners entirely, you can use an engineered expansion joint, and depending on the grout color you choose, you may be able to match it or at least come close. www.schluter.com makes a range of them. You should caulk all changes of plane and dissimilar materials joints of you don't use an engineered joint. check out www.johnbridge.com for more help on tiling.
As to cutting the tile, you have several options - if all of the cuts are just straight, a quality snap cutter works well. Note, dull cutting points and cheap designs will give less than optimal results. Cutting that large of a tile requires a big cutter or wetsaw. Also, large tile often are a little warped, so this makes it easier to have them crack as you cut through since they may not sit flat on the surface (cupped or warped), and when you get to one end, it isn't strong enough to support itself when you make the cut at the end. Be prepared with some spare tile. Lippage on large tile can be tough...you may want to consider one of the engineered leveling systems. two that come to mind are Tuscan Leveling System and LASH system.