Congratulations on your new assignment.
Cell Phones, if you are issued a cell phone by your command it will usually be serviced by TIM with free incoming calls. If not Vodafone is the way to go, they have prepaid and they also have plans. Being a mom of 3, I went with a plan (never wanted to be in a situation to run out of money on my phone), I pay 15c per minute with no monthly fee.
Home phone works great from the support site, it is 4c a minute to call home (USA), many people also have Vonage, $15-$25 per month all the calls you want to make and a local call for your family and friends to call you is also an added bonus. Skype as someone said is also a great way to communicate.
We all live in apartments on base no more than 3 stories high, some have 6 in a building and others have 12. These are quite spacious for your size of a family, supplied with a microwave, washer, dryer and a fridge. Living of post can be quite expensive and utilities are quite high on the economy. I would suggest you bring your furniture from the USA, you may see somethings you want to buy here but (just my opinion) things can be more expensive here. Patio furniture is expensive so if you want a little table on your balcony I would say by in the sales now ;0) There are parks on every corner for your little one, a great place to meet friends. There is a bowling alley, movie theater, NEX, Commissary, food court, hospital, post office, auto port all at your door step and all within walking distance to the apartments. I really think it is a good choice to be here with a little one.
I strongly advise you to ship your own car if it is in good working condition. Buying a clunker here is usually (not always) priced well above what it is actually worth, however your car insurance will triple regardless of the vehicle. The military will ship one vehicle for you. You can buy gas coupons from the NEX to offset the high prices they charge here.
When it comes down to child care, take the advise and call the CDC, it is good to get your ducks in a row ahead of time. They will also have a list of home daycares (I believe) Also I know you mentioned your little one will turn 3 soon, at some point in your tour you will be eligible to apply for the Sure Start program at the Elementary school. Your Child has to turn 4 before Sep 1st in order to qualify so maybe you can keep that in mind for the following year.
You will not be the only single mom here, you will have plenty of support and please do not hesitate to ask questions. This forum has some great people on it that give some great advise.