I find that Republic plays very similarily to Empire. Minus the massive amount of Jedi.
I strongly suggest you get one of the two Thrawns out there. The first from Universe grants a +3 to attack and a +3 to defense to all allies and, at the end of his turn, can swap two characters with each other that are within six squares of Thrawn, if they have the same base size.
The other Thrawn from IE gives Opportunist and has the same swap CE. The IE one is easier to get though because it's a rare while the other one is a very rare from Universe.
Also get Mas Ameda if you don't already have him. Mas combined with Thrawn for swapping all over the map is becoming very popular and effective in tournaments these days.

If you want tempo control, I suggest you get Admiral Ozzel. His CE forces you to activate only one character per turn, but it helps out activate your opponent and he gives 20 points of reserves if you roll a 6 for initiative.
Also, Moff Nyna Calixte's CE gives Super Stealth to any characters that already have stealth. If you use her, I'd suggest a combination of Shadow Stormtroopers (uncommon, LotF) and/or Storm Commandos (rare, A&E).
One other commander I find useful is Darth Vader, Imperial Commander. His +6 to defense has unlimited range and can make even plain stormtroopers hard to kill, but it's only for non-unique followers. Combine this Vader with the Felucian Stormtrooper Officer and you can have a stormtrooper with 30 defense in cover.

I don't think it would really be a priority. Mainly because not many are used competitivly (because of cost and it's hard to get). If you're planning on going with Stealth or Super Stealth, Shadow Stormtroopers are good and much easier to get than a Storm Commando.

Storm Commando's effectiveness combos the majority of CE's and SA's than Shadow Stormtroopers. If planning for an effective Imperial Stealth or superstealth... storm commandos are a plus because of the tools it can provide, like a swiss army knife

Not necessarily, the I believe the Rebels/New Republic has the actual control on activations, particularity Dodonna... switching Tempos of either 1 or two activations while the Empire has the real Initiative control (aka Master Tactician).

You were probably told this for the Republic, but Mas Amadda can be a very useful piece for the Imperials (Empire, always bother me too!). Very handy with Thrawn. I've seen him used with Imperials a lot more than with the Republic.

Thanks for the replies. So other than the pieces already mentioned, anything else I should look out for? Thanks

I do check the ratings, but sometimes I feel its better to ask others because occassionally the ratings aren't really in line with their playability (e.g. the Order 66 Palpatine and Revan seem to be ranked higher than what people consider to be their "playability" while Yobuck is kinda low for something that commonly used), and sometimes some of the pieces, while good, may only be played in niche squads or on low priority in most squads (e.g. Storm Commando).

For Cs/UCs/cheap Rs/VRs, I'd keep an eye out for the following:

Elite Snowtrooper, Elite Stormtrooper (UC, RS) - Good, solid troopers. While their popularity may have waned since their release, they can still pack a bit of a punch.

General Veers (R, RS) - He grants Accurate Shot, a great boost to nearly any unit

Stormtrooper (C, Various) - The basic Imperial grunt. He's not the best shot, but he's cheap, well armored, and can be beefed up by quite a few CEs.

Stormtrooper Commander (UC, UNH) - His CE gives one of your non-uniques a good damage boost. He's also a decent attacker himself.

Coruscant Guard (C, CotF) - Cheap and durable. He makes for a good support unit, either by soaking up shots or assisting in wittling down the opponent.

Death Star Gunner (UC, A&E) - He has Splash, giving him a good chance of inflicting damage on high defense units.

Imperial Governor Tarkin (R, A&E) - Extra Attack for commanders, always a plus. And his Doctrine of Fear can help if the enemy gets too close for comfort.

Evo Trooper (UC, FU) - Another good mid-cost trooper. His big draw is deceptive, which when coupled with Thrawn or Piett's Opportunist, can leave a mark.

Felucian Stormtrooper Officer (UC, FU) - Excellect defense boost for your troopers.

Moff Nyna Calixte (R, LotF) - Superstealth for the Imps

Noghri Commando (UC, LotF) - Great first-striker. A popular choice for swap squads.

Shadow Stormtrooper (UC, LotF) - A solid stealth unit for the faction

Darth Vader, SotJ (R, KOTOR) - An anti-jedi Vader. With Djem So, Riposte, and Jedi Hunter, he can make quick work of opposing force users. His main downside is a lack of defensive powers and abilities beyond Dark Armor.

Imperial Dignitary (UC, IE) - A diplomat than can attack and damage without outside assistance. Quite annoying.

Moff Jerjerrod (R, IE) - Great for swarm or gunner squads as he doubles the bonus for combining fire.

Shocktrooper (UC, IE) - He's got Missiles 30. A good way to aggravate an opponent.

Thrawn (Suffering Succotash) (R, IE) - Much cheaper and easier to obtain than his Universe counterpart, he gives Opportunist to everyone, controls initiative, and can swap units. All in all a great commander.

Disciple of Ragnos (C, JA) - Good amount of instant damage force powers.

Imperial Sentinel (UC, JA) - Big and meaty with a strong punch to boot.

One other thing, if you want a good Vader, pretty much any Vader from Universe onwards will work well. They all have their strengths and weaknesses but are all good, solid choices to build a squad around.