You can upgrade in any order you want.
But, there is a specific order that is correct to follow if you want to acheive the maximum benefit from the upgrades. That order is TT, then arm, then cartridge.
The cartridge is limited by what the TT and arm will allow it to do, and the arm is limited by what the TT will allow it to do.
I think you have the right goals in mind, as far as the gear you selected. If you want to proceed out of order, but will end up where you want, that is okay too.
But, there is a specific order that is correct to follow if you want to acheive the maximum benefit from the upgrades. That order is TT, then arm, then cartridge.
The cartridge is limited by what the TT and arm will allow it to do, and the arm is limited by what the TT will allow it to do.
I think you have the right goals in mind, as far as the gear you selected. If you want to proceed out of order, but will end up where you want, that is okay too.