On the phone situation, there is no way around this one. You cannot call her. Inmates initiate all outgoing calls, and there is no direct dial in. If you are at work when she calls, those calls are going to get missed until you work out a better window with her. The only fix is communicating a schedule to her through mail so she knows when you are actually available to pick up.
For the cheapest phone rates, InmateAid's discount phone service is worth setting up. Depending on the facility and carrier, it can cut your per-minute costs significantly, which adds up fast over a long sentence.
On letters, you do not have to use InmateAid. A pen, paper, envelope, and stamp work fine as long as you have her correct mailing address and follow the facility's mail guidelines. That said, if you are short on time or writing regularly, the InmateAid app makes the whole process fast and straightforward. When you factor in the cost per letter at volume, it comes out to less than a dollar per letter including postage. For someone juggling work and everything else, having it handled through an app rather than a post office is worth something.
The main thing to nail down right now is getting a letter to her that tells her when to call. Once she knows your schedule, the missed calls stop being a problem.