The problem is there are a LOT of frequencies to jam, which takes a lot of power and jamming equipment, so that's not practical. For this reason, once they take out the cell and internet capability, I suspect it'll just be radio direction finding equipment and targeted strikes against anyone who transmits, either via soldiers, or perhaps via a missile or air strike.

So I suspect the first thing to go will be the cell phone network and the internet. This'll take out 80% of the general public's communications ability, as a lot of people don't have land lines any more. Next up in priority would be the civilian law enforcement and emergency responders communications, although this will be harder to do. They'd be the closest thing to an armed and trained paramilitary force to be dealt with if you're trying to take over a country, hence the priority. Military frequencies would also be a jamming priority, but are going to be exponentially harder to do, as they are hardened and expect jamming so they frequency hop and use other technological schemes to make them hard to jam. Finally is ham, but there are so few of them relative to the population that they'll be low priority. Most likely they'll be targeted by direction finding equipment as mentioned above. I don't believe CB, FRS, and GMRS will be paid much attention to because they are so short range as compared to the others.

The POTS (plain old telephone systems) will also be hard to take out, as it's somewhat hardened, and very distributed. You'd have to know exactly which relay stations to take out, and where they are, and take out all of them for a specific area to take down telephone communications to that area.