Is it Beastmaster as in the 80's film and a lot of different creatures. Or does he just get the one companion upgraded?
You choose one companion at level 3 and keep it until it dies.
The PHB was built actively trying to avoid making the Beastmaster two PC's in one, keeping the companion weak and requiring direct input from the PC to do much (ie PC has to use action to make companion attack). The companion doesn't scale well as you level up - which IMO is the main problem with it - it doesn't get any more HD, and its ability scores remain the same. So the upgrade is quite poor.
The UA version tries to make the companion much tougher and better at the expense of the PC. Eg the beastmaster doesn't get the Extra Attack feature, because the companion can attack on its own. So the upgrade requires you to use the companion fully as it is most of the power in the class.
When I first envisioned the character he should have been a mounted archer, but the PHB companion was too weak (though in retrospect probably would have been fine for the duration of this game) and the UA version doesn't give the PC the crucial Extra Attack to make fighter types not rubbish.
So with the UA ranger in mind I built the character to be a lancer, charging both companion and character into melee, with a devastating opening attack with a lance and the companion doing his own attacks. Then I noticed that the lance has disadvantage on targets within 5' of you, so the character and companion couldn't both be in effective range at the same time.
So Simply dropping the lance and using a saber, seems like the simplest solution