First of all, I agree with the above post that what you are requesting is a very good thing. Far too many members leave their spouse in the dark, and it only results in problems in the long run.
If a soldier is single that's fine, but if a soldier is married it is much better to have full support from home, so any initiatives you have to keep that support are to be applauded.
To answer your question, the above responses so far generally cover it. Here is a consolidated list:
1. Cell phone. I would recommend it as you can usually use it unless you are in the field in a tactical environment. Don't expect to be making calls every break, though. Also, most carriers are okay with you changing your number for free if it is because of a military posting, so you're only getting charged for long distance instead of long distance + roaming (if you still have your old number).
2. Pay phones. Most shacks have them, but expect line ups if you are doing the calling card thing. A floor of 100 candidates may have two phones.
3. Wifi internet. Don't count on it. If you are semi-qualified and on some sort of year-long course where you are in enhanced accommodations (vice "shacks" with 4-32 per room) then you could potentially order it, but for most courses it's "no".
4. Army-provided internet. Very base / course dependant. Some buildings have computer labs where you can use Army computers, but not all websites are allowed (no hotmail, g-mail, etc). This is not assured either, but if you get an Army e-mail account it would be possible to use on weekends that you have off.
The other points are valid that your evenings are more than likely going to be filled with things to do like ironing and studying, so if you are allowed a cell-phone that you can squeeze a call in for a few minutes, that option is better than waiting in line for a pay phone or going far away to write an e-mail
