I was wondering what companion would be best for a character with Unarmed, Survival, and Speech tagged. I was thinking Raul because of his regular/full maintenance.

That doesn't make much of difference. Companion preference rather depends on your play style. Sneaky? Storm trooper? Pacifist? Don't-shoot-unless-shot-at?

Now it just looks like you got a companion you want to use and want us to confirm that liking. Sure, use Raul if you want to use Raul. If you don't want him, kick and get new one.

Veronica or Cass, they are friggin' good when attacking with melee/unarmed.

Veronica with Pushy and you with Ballistic Fist own everything hard, the same going with Cass if you give her Knock-Knock or a Chainsaw.
With Cass you also have her perk, wich adds protection and if you did her personal quest raising her damage output, she kick some serious a**.

I just run forward and punch stuff.

its all your preference.

Any unarmed character would be great with another unarmed/melee companion like:
Lily, Veronica, Cass. Rex
OR, have an opposite character to be prepared for every situation like;
Boone, Raul, Arcade, ED-E

Yep :turtle:

I'll just stick with Raul so I don't have to get my stuff repaired as often.

You and a certain female brotherhood scribe might get along

I'd say stay with Raul and give him a Brush Gun. He can take on any enemies from afar while you take any that rush at you. Like you mentioned, his perk is really useful (rather than a certain moody sniper -cough, cough-).

Raul is the best, and once you upgrade(finishing his quest) him his perk becomes way better.

I'm just going to use her for Scribe Counter. If I could get HH I would have her wear the White Legs hide armor and walk around my Lucky 38 suite.

Actually I'd not take Veronica for unarmed character - it's better to have just one keeping the enemy busy at close range while someone gives support from afar.