What Adrian says about the width of the tenjin is true, but replacing the tenjin or the neck is going to be more trouble than buying a new cheap shamisen.
My advice is to keep the instrument you have, replace the strings, the koma, and possibly the kamigoma. If the kamigoma you have works with proper strings (if it doesn’t buzz or dampen the sound) then leave it as it is; if it doesn’t work, replace it with a small strip of bone or hardwood. I’ve used sections of bamboo chopsticks, filed down and shaped for the purpose, as kamigoma on kankara sanshin.
The neo you have now looks like it will work, so there isn’t really any need to upgrade. Then just start playing, and if you keep playing, at some point you’ll buy a better instrument. I’m a firm believer in making do with what you have at the moment.
Seconded, Gerry; I’m totally all about upgrading when you need to.