I am fairly new to the game (~2 weeks now) and I haven't tried to follow any of the episodes. I was curious if only being a LT. Comm. Grade 5 would be too low to start them. If there is any feedback you can give, it would be greatly appreciated. Also any other odd ball tips would be great as well!
Simple question, simple answer: you can do any mission whenever it is available.
Some of the featured episodes give special rewards which are rank specific. So when you get to a higher rank you may want to do the mission again in order to get the higher ranked reward. Other then that you can do them at any time.
Generally speaking, when you've reached the level at which you're eligible for a mission, even the Featured Episodes, click J to bring up your mission dialog. At the top are a few tabs. Click on the tab on the left top that says "Available." It'll show you what missions you don't already have (that you haven't done previously) that you're able to take at that moment. Featured Episodes fall into this category as well.
Most story missions and such are repeatable, and some of them show back up under your Available tab, usually the exploration missions, and daily missions. Many don't. Featured Episodes and Story Missions are examples of those that don't. To retake those if you've already done them (like to get the next tier of the Breen Absolute Zero set, for example), you go into space, click the little triangle on the bottom right of your minimap, click Visit Bridge, and when you're on the bridge, go to your Ready Room. There's a computer console in there that'll flash, and you can select from mission that you can retake. You take the missions you want to take, and they show up in your "In Progress" tab on your Mission dialog.