Personal characteristics: They are technically required, but I will be honest: This stuff is sort of tacked on, the books don't do a great job of actually answering the "or something", and aside from a few clever bits in the DMG it barely interacts with the rest of the system. It's one of the weaker points of 5e, in my opinion. What they are fundamentally supposed to do is that I, the GM, give you a goodie when I think you've portrayed your character well. It doesn't really get more concrete or complicated than that.
For our purposes, you can treat them as optional if you're having a hard time filling them in, or leave them blank for now and fill them in later.
Equipment: As already noted, you get starting equipment from your class and background, which generally give you what you need starting out as a member of your class, objects from your background for flavor, and some starting pocket money. If you want, you may choose to forgo these and buy your starting equipment the hard way (in this case, just take the average of the starting gold roll). If you're starting with the class and background kits, you may also buy extra things from the equipment list with the starting gold from your background, if you wish.