[quote=Risewild]
Welcome to the TTW community
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When you install TTW you don't need to run Fallout 3 at all.
TTW is a Fallout New Vegas mod so you have to run Fallout New Vegas to play it. The installer only needs the Fallout 3 files so it can convert them to be usable by the Fallout New Vegas game, after that you don't need Fallout 3 anymore (except when you reinstall TTW or install a new version of TTW).
TTW starts in vault 101 with the "be born" sequence by default but, there is a addon/optional TTW file (called TTW Startup Menu) that allows you to choose where to start (it pops up a window when you start a new game with the options of starting in the Capital Wasteland or New Vegas). You can find the updated version of the addon here (the TTW installer one is outdated but we will include the new one in the next TTW update). Just install the TTW Optionals and then replace the old file with that new one and you should be ready to start in NV.
If memory serves me right, when you use the TTW Startup Menu optional (the one I linked before in this post), you get a few items and messages after you receive the pipboy from Doc Mitchel, if you read, look at and/or listen to them it will link the Courier to the Capital Wasteland and you will get a quest to go to the Capital Wasteland to find your dad (FO3 main quest). My memory is not the best and I haven't looked at that optional file in years, so I might be remembering it wrong though. 
So some work have been done to link the Courier with the story of Fallout 3 if you use the optional file. 
Hope you enjoy TTW
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Well I also thought about the possibility instead of linking the Courier with the Lone Wanderer, what about the possibility of having them as separate characters, and when you play as the Courier, "Dad" is simply referred to his real name James and instead of "Finding your Dad" it'll be more like "Find the sources of a mysterious radio broadcast from a man named "James" when you're in the Mojave and plus there could be dialog changes where James refers to his son or tasks you to find him which is the Lone Wanderer (I think there could be a way to reach out Fallout 3's save game and use the character you generated there which also effects James) which becomes a companion I would think.