I'm looking for some advice on how to go about making the best Wookie Heavy I can make, ideally with either a Light Repeating Blaster OR a Rocket/Missile Launcher. Hired Gun(Heavy) is an obvious choice but I'm unsure of what other specializations, if any, to pursue.

Define "best." What all would you like your Wookiee to be able to do?

I think the Heavy specialization eventually gets the most out of auto-fire. Otherwise, it is all about carrying around the largest weapon you can that should otherwise be on a tripod.

He's a former pro Smashball player and was a Shockboxer before turning to mercenary life when his career was cut short. I'd like him to be personable, and athletic, as both would be needed as a pro sports player and also well versed in most forms of combat. Brawl, Gunnery, Light and Heavy all seem pretty appropriate, as well as stuff to make him somewhat charismatic, if even only intimidating. He's currently a mercenary working for the Hutt cartels as muscle after he had gone into hiding for killing someone accidentally in the ring. He's been a professional soldier now for roughly 5 years.

Marauder with a Brawl focus would be a good fit.

Agree Marauder. Would round him out nicely, lots of good defensive talents in their as well as some cool close-combat stuff.

Also if you want him to be intimidating, Coercion is the skill for you. Be sure to spend that measly 20 XP to boost your Willpower up to 2.

If you do eventually want to pick up a LRB, bumping your Agi to 3 at character creation wouldn't be a bad idea, but you don't need heavy to be good with a Light Repeating Blaster. For this reason, I stand by what the others are saying, Marauder.

I'm looking for some advice on how to go about making the best Wookie Heavy I can make, ideally with either a Light Repeating Blaster OR a Rocket/Missile Launcher. Hired Gun(Heavy) is an obvious choice but I'm unsure of what other specializations, if any, to pursue.

If by "personable" you seriously want to pursue that mechanically in the game, as opposed to just role play him that way, I would go Mercenary Soldier in Hired Gun to paint him in the broadest stroke possible at creation. You have a blend of talents that lean both combat and presence oriented, as well as, all the combat skills as career skills. Then branching out from there would be a possibility in the Hired Gun career.

I'm going to go against the grain and suggest that Marauder isn't a great secondary specialization for the character you've described. I think that Enforcer fits better.

Here's why:

Marauder is a great specialization to kick ass with, but if you are toting around a big gun, you want to use that gun. So the Frenzied Attack and Feral Strength talents won't be terribly useful most of the time. All of the talents are focused on melee destruction. Even though you get Coercion as a skill, you don't get access to any talents that back it up.

Alternatively, Enforcer gives you Brawl, Coercion, Knowledge Underworld, and Streetwise (which a Hutt strongman should have). It also gives you Intimidating (to better your Coercion checks) and Fearsome (people are scared to get close to you). You'll get access to a few defensive talents, you'll get Talk the Talk and Walk the Walk which both seem like they would fit the character. There is Loom which is an interesting sort of side talent that could be useful to your party's face character. Free Advantages on Charm, Deception, and Negotiation? My Scoundrel suddenly wants your Wookie there during all the social scenes. Instead of being dead weight in the non-combat stuff, you'll have something to contribute.

Enforcer won't make you as much of a combat monster in close quarters, but you will still be a force to be reckoned with in a bar fight while bringing a wider range of abilities to the table.

Edit: 2P51 makes another good suggestion. Hired Gun would make you a strong leader and Field Commander is one of my favorite talents in the game thus far. I'd suggest Bodyguard as another reasonable option; with three more ranks of Barrage and plenty of defensive talents. Brace is in the mix as well which may or may not be useful depending on how your GM runs it, but they aren't requred talents.

If you wanted to max out Auto Fire then you should look at picking up Jury Rigged to get the activation down to one Advantage. Such as the following:

Ace: Gunner - also has Overwhelm Defenses which would make gunnery misses interesting

Bounty Hunter: Gadgeteer - If you also want to max out your armor, soak, and hard points

Technician: Outlaw Tech - also for upgrading weapons