I'm more of a HFT guy than FT but I actually use a FT stock for my HFT gun and I'm seriously thinking of shooting FT with it.
You'll drive yourself mad asking what's best between a TX and a HW. They are both capable. HWs with a tune is my choice.
My only additional advice is that you'll probably end up wanting whatever you buy in a custom stock. Probably that adds more weight and has a higher cheekpiece, or an adjustable one, and some sort of added depth to the fore end ( hamster / palm rest etc ). So I'd look to buy an action s/h and then spend money on a stock that fits you. However 2nd hand 0.177s are either a decent price or get snapped up quickly.