I think you can get away with what you have - but only if you are going to do one batch at a time, and only if you are going to do all extract OR a partial mash with a tiny amount of grain added in. If you find you like brewing trust me, you'll want to get more equipment, starting with a much larger brew pot (minimum 5 gallons/20 quarts).
Also you may not want to tap both buckets as bottling buckets - I've got a problem letting yeast site in a spigot/grommeted piece for too long, afraid you may devolop a situation with that bucket.
So in closing:
3 gallon stock pot (SS hopefully) - extract brewing or minimal PM
6.5 gallon bucket - fermentation vessel
6.5 gallon bucket - bottling bucket
Growlers (enough to "bottle" 5 gallons of beer
If you do it this way, you'll be able to stagger your brews and have 5 gallons of beer initially in six weeks then every four weeks following (assuming you made a basic ale).
The brewing schedule would go something like this.
1.) make beer, put in primary for four weeks
2.) transfer beer to bottling bucket, add priming sugar, bottle in growlers. Simultaneously start new batch of beer.
3.) let beer in growlers sit for two weeks, then begin consumption.
4.) two weeks after you start consuming beer, bottle second batch, and brew third batch.
I've just brewed 11 gallons of a blonde ale two weeks ago (5gal and 6 gal), those are getting transferred to secondary tonight so I can start a 5 gallon batch of a Heffe and a 6 gallon batch of pinot gris wine.