I would recommend Romeo Y juliet, those are great cuban cigars yet not very harsh! Or maybe Partagas a bit stronger but so is the flavour. As to cutting it, it really is you preference some will cut with a cigar cuter with usually means cutting the tip off. Me i like using the cutter that just cut a groove (like a piece of cake) or the thing that just cuts a hole in the tip of the cigar.

I wouldn't recommend relighthing a cigar later.... It is normal to relight a cigar during a smoking session but letting it burn out (by the way alwais do that never put it out as it will stink) and keeping it for later will just make sure that the cigar will taste like shit!

And the best place to keep a cigar (apart from a humidor) would be in the bathroom, humidity will make sure the cigar stays good... if you buy a humidor then humidity should be around 65-70% and make sure you use distilled water to soak the sponge or else you have some mineral deposits and it will alter the cigars taste... Have fun smoking you Cigar!