A new AGM battery can be purchased on Ebay.
You may not need to clean the carb. Fresh gas may do the trick.
But if you do, you can clean the carb yourself, or take it to a Yamaha shop.
Download the TW manual and supplement:
To start with:
Drain the fuel tank and carburetor. Put in fresh gas.
Change the oil and filter.
Install new battery.
If you're lucky, the bike will start without doing anything further.
(Check the manual for the starting procedure.)
You will still need to check over all parts of the bike: chain, tires, etc.
Look in the manual and check all the "Scheduled Maintenance" items.
You said the bike has only 100 miles on it, so the engine isn't broken in yet. Ride it easy (vary speed) until you get to 500 miles There are many different opinions on breaking in an engine. Go by the manual.
Since you are new to motorcycles, it would be a good idea to take a Motorcycle Safety class.
And buy some protective gear: helmet, jacket, boots, gloves.
If you are going to ride the "back country", it's best not to go alone, or have a way to call for help, and take basic tools, and a small survival kit.
Then enjoy your new TW.