I like doing things as inexpensive as possible but doing it right so it turns out tasting great.
If the Culligan is PETE1 carboy then great! If it is another number then no.
The Skeeter Pee directions call for you to use a wire wisk to get air into the primary. I did this and it fermented right away. If you start in a Carboy jug then you cannot wisk it daily.
I'm using 5 gallon food grade buckets from Lowes for primary so I can wisk air into the SP. They are $3.97 each but if you buy 5 you get the "contractor pack discount" for $3.45 each. Then if you go to the post office beforehand and get the moving packet there is a 10% off coupon. They also sell the food grade lids with a seal for $1.45. So you could get a couple of these and then when it's time to go to secondary you could fit an airlock in the lid.
Personally I like using a carboy for secondary. I prefer PETE 1 plastic carboys over glass. I like the plastic Better-Bottle but a less expensive route I also use is to get a 5 gallon NESTLE brand water bottle from the grocery store. Just make sure the water bottle is PETE 1 and not another number on the little triangle on the bottom.
After secondary I am putting it in Corny kegs and charging it with CO2 to make it carbonated.