I tried an alto years after playing tenor and the transition was a breeze… all saxes are the same, and …..all saxes are different!
what you have learned on alto will definately transfer over to tenor… embouchure, fingering etc…all the same.
the mouthpiece is a different story.
you will need to experiment a bit. not knowing your playing etc I can’t tell you if starting off with a metal mp is good or not at this point.
Dukoff’s and Otto Links are what I played before I discovered Guardala’s. It’s a big jump money-wise but in the end you will probably want one.
for now just get something that you think is comparable with your alto mp opening etc cause if you’ve been blowing an alto for years with a small opening jumping to a wide metal mp on a tenor sax would be too much of a change and might turn you off.
let us know how you go!