Glad to hear another Buell is about to hit the road! An '06 with only 600 miles!?! Oh wow. She's gonna need some love.
The well-meaning family members probably did more harm than good by treating it that way, but it's not the end of the world. Buell's are super strong and stupid simple.
If you are feeling "overwhelmed after reading the service manual" I would suggest finding a good V-twin shop in your area. But, if you want to attack it yourself anyway:
The manual spells out every procedure step-by-step. Don't dwell on everything all at once. Pick one, like an oil change, and read through it until you're familiar with the procedure and do it. Next, pick another one and repeat.
So:
Change the oil. Use the correct weight of the lowest temp you will ride in found in the chat in the manual. Typically 20w-50 for most of the US. Use a synthetic V-twin specific oil.
Change the Primary Fluid. IMO Buell stock clutches like Harley "Formula +" or the Amsoil Primary fluid. You can use 20w-50 in there as well put I think it gets grabby.
* Most important: Drain the gas. 1/8"MPT plug in the fuel pump flange. I would also remove the pump completely to check it's condition and flush the tank. There's an easy cheat to have it out much faster than the manual procedure. Once the pump is all together, you can flush the system yourself by screwing a fitting onto the schraeder valve on the fuel rail (pics in the manual) and (key-on) using the pump to purge it into a bottle. Hopefully you don't need the injectors removed to be cleaned, but this should be enough to get it running reliably.
If the tires are 7 years or older (4 years for sport tires) I would change them as well. Removing the wheels off the bike will save some labor cost and get new wheel bearings too. While it's on stands, polish the fork tubes, and as much of the rear shock shaft that you can. Leave a thin coat of oil on them all.
Flush the brake fluid front and rear. A vacuum pump is a simple way to do it without having to bleed the system.
You'll probably want a nice, new, battery. Buells are hard on them. 220CCA minimum. They don't like cheap batteries. Make sure the terminals are tight and while you are under the seat, make sure all the other wires are tight where they screw into the seat rails and there wasn't any critter-issues under there.
All that should be enough to simply and cheaply get it running and see how she is. Theres many more things you could do (like fork seals) but 5 years isn't a decade so get it running first and see what pops up.
Good luck!!