I use a speakerphone, with my laptop sitting right near to it so that the phone picks up the laptop's speakers well. This works quite well.
I can be listening to the other person, and typing away at the same time, so that when my turn comes I can "talk."
I have tried having a conversation with a "normal" (non-speaker-) phone,
but it is very difficult. You have to listen to the other person, then set the phone down next to the laptop and type and "speak", then pick up the phone again - very awkward and difficult to pull off, and especially if the person goes on speaking after you have set the phone down, and you miss what they said. Embarrassing.
Regardless of which type of phone is used, or in fact regardless of anything at all, there is a problem with using TFM in a conversation, particularly when there are several people involved, and not just two. That is the problem of interruptions. It is all too easy to push the "Talk" button and have a little pause while the computer gets its computation done in anticipation of speaking; then the machine starts to speak, but in the meanwhile the other person has started to speak too, so the machine interrupts rudely. Even the Stop button takes a little while before it starts to operate, so this is quite a problem. The only way I have found to solve it is to raise my hand, like a grade school student, when I have something to "say" - then people have learned to be quiet and wait for the machine. But it means you have to train everybody you have a TFM conversation with.