TFH, I'm thinking of hosting a Lt. 1 Pakled DSE run later this week. If you have the slot, create a Pakled, 'make him go' through the tutorial, and prepare to RP the historic encounter of the first Pakled's to meet a Klingon Battle Fleet.
It would be glorious for them...if it wasn't so sad....
You'll leave the first sector sometime around Lt.5-6. I think the next sector is the Regulus Sector. Once you finish that sector, you should be Ltcomm 1 and you'll move into the next (against Romulans I think). As you level up and complete missions in different sectors, you'll move on. It's fairly linear as far as Episodes go, but you can always go back and do patrols etc in lower level areas.
Your missions eventually start to guide you out of the Sirius Sector through "Patrol" missions and a few episodes; The Kuvah'maugh (spelling check?) for instance, which directs you to the Regulus System in the Celes Sector, in the Regulus Block.
Usually the mission text will tell you what Sector Block you need to go to. Each Sector Block has three-four sectors within it. The easiest way to navigate is to hit "M" on your keyboard to bring up your map, then click on System List. The System List will have all the systems/other locales in your current sector block that you can visit and it will also have the the other Sector Blocks that are connected to it.. I think they're denoted by a triangle on the left side of the name.
Just double click and it will auto-navigate you to the sector border for that sector block and a "traffic control" officer will prompt you to warp to the next sector block or cancel. Sometimes you have to pay careful attention where it's trying to send you, because if you hit the border too soon (before you reach the sector you want) it will try to warp you somewhere else. For example, if you set course for Beta Ursae from the Sol System it will try to send you to Delta Volanis before you get there because of the pathing.
If you look at the Galaxy (I think it's called) tab, you can see how all the sectors blocks connect, so you can see what sector blocks you need to take to get to other sector blocks. For example, to get to the Pi Canis Sector Block you have to first go to the Regulus Sector Block.