Years ago I used to hold the base in my lap with one hand and fly with the other, using the hand that held the base to operate the base mounted controls.
A while back, I took to leaving the stick on the desk, to the left of the keyboard, I still use my off hand to operate the base mounted controls. I have MOST flight keys mapped to the stick, along with the text radio keys.
I found that leaving the base on the desk resulted in more consistent and reliable control inputs.
I'm using the latest of the Saitek Cyborg series, the EVO Force. It has a bunch of buttons, and it fits my left hand well. I use a headset to avoid having the rest of the house being bothered.