As Wermie says,a size A or possibly a B size tool post will fit your 10" lathe. The piston type is always cheaper. The wedge type is better,but for the size and power of your lathe,the piston type will be far stronger than you need. Unless you are trying to make money mass producing lots of the same parts,don't worry about repeatability. And,if you are,you should be using a CNC anyway.
The wedge type tool post sucks the tool holder toward itself. Then,the wedge,dovetail surfaces jam tightly together,but,the flat surfaces on either side of the tool holder such up tight against the tool holder. All the surfaces are in tight contact with the holder. The piston type pushes the tool holder away from the tool post,so only the dovetailed surfaces are in tight contact. It is less rigid,but your lathe is not powerful enough to cause appreciable flexing of the tool holder.
I was stubborn for years,thinking the old lantern type tool post was more able to get tools into various corners,etc. I even made a hardened,very nice lantern type post for my 16" lathe. Lapped the threads in. No slop at all.
But,when a used Aloris came along,I got it and a bunch of holders from a company that went out of business. The improvement in rigidity was huge!! I never use a lantern type at all any more. You will not look back either.
Dropping on a pre adjusted tool that is set for the perfect height is so much faster than diddling with a lantern type,OR those 4 position blocks that import lathes seem to come with (I use a lot more than 4 tools!). You have to shim those up to height,too.