Starting planet gets to around level 10 for most people (some who skip a lot can end up levels 8 or 9, while some who like to do EVERYTHING including Heroics a few times, and is a subscriber, with EXP boost, can end up at level 11-12 before leaving starter planet.
Generally, it's level 10, where you get to your faction's Fleet Station, and everything is unlocked to you, including your advanced classes.
It takes an average person about 4-5 hours to finish the starting planet, and about another 5-10 hours per planet if you do everything.
If this is no longer your first, you're properly funded with equipment and mods, credits, etc. and know what you're doing, you can probably blast through each planet within 2-3 hours (by skipping almost all side quests). In total, there are I think ~10 planets for your main stories, and a few more faction/class related/restricted ones.
There are 3 main types of quests: Main Story quest, related to your character and class; Planet Story quest, everyone in the same faction goes through, but is a long series of quests that brings you to most areas on the planet, which after you're done may or may not lead to a Bonus Series, which continues even after your Main Story on the planet is finished with; Side Quests which are completely optional. This also includes many Heroic (Group Missions) Quests and Flashpoints. Some can give great rewards, while others are just there to... waste your time, and something for completionists *raises hand* to do
For a subscriber, after leaving the capital planet, and gain a few easy levels with space combat (the on rails one) that takes 30 mins/1 hour to get to level 20, it's only necessary to keep yourself boosted with the EXP buff and only doing Story quests and Planet quests, yet you still outlevel the quests given to you. Free to Play characters are unfortunately forced to do almost everything including occasional PvP and Space battles (although limited per week) to keep up with the levels required.
wow... I wrote a lot