Been there done that. I had the same dilemma as you. Although I am playing Empire and these are all the information I got for that faction, I believe there are similarities with the the Republic.
Daily Quests:
11 Quests on Belsavis:
- Ancient Transmissions
- Deadly Mutations
- Droid Malfunction
- Found in Translation
- Invisible Threat
- The Carriers of Xenovirus Prime
- Reluctant Volunteers
- Unintended Consequences
- Freeing the Fallen (HEROIC2+)
- Old Enemies (HEROIC4)
- Lights Out (HEROIC4)
6 Quests on Ilum:
- A Tightened Grip
- Defend the Shipment
- Operation Shatterstorm
- Sabotage
- Rightfull Owner
- Poisonous Strategy (HEROIC2+)
The Heroic quests, offer you 3 daily commendations and item modification mods, in addition to the pile of credits.
PvP:
First of all, head to Combat Training quarters in the Imperial Fleet and get your daily and weekly PvP quests from the Quest Ternimal. There are 2 kind of quests, Open World PvP and Warzone. The warzones are pretty simple. On the other hand on a low populated PVE server, there isn't so much fuzz on the Open PvP areas. The quests you will be needing to do, is to cap bases (example in Ilum) so you can complete the quest. But you wont be able to complete them, if no one from the other faction caps them again. One solution we found is to talk with the opposite faction players through /say chat and chain cap the points.
The warzones that when you queue you can randomly join in are:
Huttball, score the ball style with fires and traps all around.
The VoidStar, defend/attack the gates till you reach the terminal.
Alderann, cap the turrets and wait for the points to get to zero.
The quest rewards are bags with centurion commendations, item tokens and credits and once you reach level 60 rank on the pvp system, you will be able to chose from higher grade pvp items.
PvE:
The only PvE you can do at the moment, are the Flashpoints either normal or hardmode ones.
Before you enter the Flashpoint, you have the option to accept the quest you need to have to enter it, in Hardmode or in simple Mode.
You can get your daily and weekly quests from the Quest Terminal located in the Supplies quarter on the Imperial Fleet.
The Flashpoints you can do and get a decent loot for raiding are:
- The Black Talon
- Boarding Party
- The Foundry
- Directive 7
- The Battle of Ilum
- The False Emperor
If you choose to do these FlashPoints, you will be able to collect from the bosses additional tokens that can be traded for PvE amour and mods.In addition, on Hardmode, you will receive additional tokens for better quality gear.
Datacrons:
Lastly the beloved Datacrons that can be found all around the planets for a marvellous of +4 stat.
Crew Skills:
Its time for you to max out your Crew skill missions and get familiar with the GTN and what type of items yo u can craft and sell. Furthermore you will need some time till you discover all the prototypes you are willing to start using and better be prepared for some credit spending :)