You don't need this Combo for this character
The Unearthed Arcana: Revised Ranger class makes its most significant changes to the Beast Conclave archetype, and one of those changes, most relevant to you, is that the Animal Companion acts on its own Initiative Count:
UA: Revised Ranger, Companion's Bond:
Your animal companion gains a variety of benefits while it is linked to you.
The animal companion loses its Multiattack action, if it has one.
The companion obeys your commands as best it can. It rolls for initiative like any other creature, but you determine its actions, decisions, attitudes, and so on. If you are incapacitated or absent, your companion acts on its own.
This is a marked deviation from how the PHB Ranger class behaves, where the companion is explicitly described as not taking actions on its turn unless you tell it to:
It takes its turn on your initiative, though it doesn't take an action unless you command it to. On your turn, you can verbally command the beast where to move (no action required by you). You can use your action to verbally command it to take the Attack, Dash, Disengage, Dodge, or Help action. Once you have the Extra Attack feature, you can make one weapon attack yourself when you command the beast to take the Attack action.
Since Suggestion already describes its effect as causing the creature to follow your intent "to the best of its ability", adding it to the UA:RR Companion's ongoing attempts to "obey your commands as best it can" is redundant. So while there's nothing stopping you from using Suggestion on your own animal companion in the way you're describing, there's also no need to: the Revised Ranger's Animal Companion is already capable of doing what you ask of it without needing to waste your Action or one of your Attacks, or needing to provide explicit instructions with Suggestion or other similar spells.
Note that the Revised Ranger does not get the Extra Attack feature normally granted to other Ranger Conclaves, and instead gains the ability to allow their companion an extra attack through use of their Reaction as a level 5 ability while the ranger takes the Attack Action. So if your goal is to allow your companion to gain its reaction attack while you also take two attacks (allowing both characters to get two attacks per round), you'll need to multiclass into another class that has the Extra Attack feature.