I'm currently stationed in Korea.
1. For phone options, the general expensive ones are around $110/mo each. If you go prepaid, which is what I do, then it's much less. I chose to go with SK Telecom, and I bought a used phone. It was $20 for the phone and initial activation, then each month you pay another $10. With that, you get 500 texts and 90 min of voice call. (Disadvantage: if you don't use the time/texts, you still pay every month. Advantage: in Korea, incoming calls and texts are not charged to your phone. So you could forget to recharge the minutes and still receive phone calls. I do this literally every month.) You can also add more cards to it at the same time, to include US calling options. As for me, I use Skype or Facebook Chat to call home, as they are completely free.
2. If you are going to live off post, you can buy cars for under $1000 easily. They aren't necessary where I live, but you will be living further south due to some changes happening with USFK. I don't know how those places are, but seeing as you're command sponsored, I'm assuming you'll be around more than a year. For that, a car will be useful, though again, not required. Bikes are really cheap from soldiers who are pcsing and need to pawn off their stuff quick. You can get really nice ones for $100 most days. This usually includes a lock and helmet, and all the requisite gear the military requires. (Just read you're going to Humphreys) Ok, so that changes something in transport. I would definitely get a car, but you should realize life is going to be fucking great down there. I wish to God and all things Army HR that I was stationed down there. It's an amazing post, and it's only getting better. I'll be helping to move my brigade down there next year at some point, but won't get to experience it for long. Any way, on post transport is readily available through free public buses and cheap taxi services. Off post, trains and buses are extremely cheap and there's a great system for using them (T-money cards). If you live on post, a car is not necessary at all and I don't recommend one. Off post, I would recommend one, especially if you plan on traveling and don't want to deal with bus/train schedules. Why not get over here and decide after a few weeks? There's always people leaving, and if there's a low supply in Humphrey's of cars, you can always hop a train to another post and buy from soldiers there. Up where I am on Casey, a lot of people are always leaving, and I regularly see vehicles for $800 to $1200. (Also note: gas is much more expensive here from what I've seen.)
Hope all that was helpful! Any more questions I can help with, feel free to PM me.