I've owned Fallout 3 for quite some time, a year or more. And played the heck out've it. Never did finish the whole Wastelands map.

My Fallout3 Mod Load List

Note, this is managed by an application called FOMM, and also I think I have one called BOSS
Fallout3.esm
CALIBR.esm
CRAFT.esm
FO3 Wanderers Edition - Main File.esm
Binoculars and Scopes.esp
CALIBRxMerchant.esp
CRAFT - Activation Perk.esp
DCInteriors_ComboEdition.esp
Slower Levelling - extremely slow.esp
FO3 Wanderers Edition - Main File.esp
FO3 Wanderers Edition - Alternate Travel.esp

Total active plugins: 11
Total plugins: 18

So my questions:

1. What is the best way to install the GOTY version so that I make installing all those mods the least troublesome? Copy the original Falout directory and rename it and then drag and drop the mod folders into the new GOTY one once it is installed?

2. Once I have GOTY running, can I start the game from one of the other DLCs instead of the Wasteland?

The "GOTY" edition is literally just the regular game and the installers for the DLC. They're not seperate, and you don't have to reinstall to just install the DLCs. Don't forget to grab the DLC compatibility patches for FO:Wanderer's, though.
The DLCs integrate into the wasteland, they're not seperate games, rather you access them through regular gameplay. The Pitt, for example, has you take a cart from the capital wasteland up to the pitt, and mothership zeta sees you being abducted from a specific point.

It looks like your DCInteriors version is kind of old, it now uses an .em file, not an .esp. You might want to update it, he's added alot to it.

Thanks guys! Cool. So that means I can just update some things, install the two DLCs and start afresh!

I'm debating whether to try to keep going with my current character, which I'd say has explored about 1/2 or more of the Wastelands, or to restart.

It is possible she has already passed the points that link to these other DLCs so I think I'll restart. May wait a bit longer till the memories are even a bit less fresh though. Ordered Morrowind GOTY too, so I'll get my fill on that one before going back to FO3.

Thanks again folks!

No, no, the DLCs are totally seperate, and with the exception of BS (Which comes in at the end of the main quest) they can all be started at any point. If you're restarting just to do the DLCs, I'd reccomend against it - they won't seem any less jarring, and indeed can sometimes make you overpowered very early in the game. I'd stick with your current game, it'll go down nicer.