This depends somewhat where you live, but you'll need a lot of new stuff to meet current code!
One of the pros can fill in any details I omit or get wrong, but generally, any counter space 2' (?) or larger needs a recepticle, and they can't be more than 4' apart - there must be two independent GFCI protected, grounded, 20A circuits for the counter alone (not shared with wired appliances), and it's a good idea to have your frig and stove on separate circuits as well as possibly the range hood and microwave (depending on wattage). Since the stove is gas, you could probably put it and the range hood on the same circuit, since they don't normally use that much current. The disposal could be a fairly good-sized load as well, since some of them are over 1hp, and it could sit on it's own breaker as well. I don't think there's a minimum distance from the sink, although there may be a practical one. I have a corner sink, so there's a fair amount of room behind it, and there's an outlet behind it. That's probably not practical on a normal sink along a wall, but since it must be GFCI protected, it's more of a preference thing than safety - you don't want the cord draped in the sink, but that could happen even if it was several feet away.
Some of the stuff can be combined, so that could minimize the new wiring. 12g wire is a pain to run as it is noticably stiffer than 14g, which is normally used for 15A circuits.