Welcome. A bottling bucket will definitely help. I cannot imagine trying to prime a carboy and then siphon to the bottles. You can do it either way you describe, but it will be difficult. bottle fillers include in most kits themselves can be tempermental and leak beer. If you do the second one, boil water, add priming sugar to dissolve, cool, add to primary and then rack beer on top of it.
What equipment will you use to bottle?
Keg 1: American Wheat
Keg2: German Ale
Next up: Christmas Old Ale, American Wheat AG, need suggestions