For the long term, you're going to want a bigger pot, if for nothing else than to make enough soup or chili or chicken stock. 4-5 gallon capacity is your goal. For the even longer term, you'll want a 10 gallon (or larger) brewing pot.
I assume that with such a small capacity pot, your kit is an extract kit? It would be difficult to do much more than steeping grains in a pot that small.
I should have asked way back, Why an only ferment 3 gallons? You can get a five gallon water carboy, use the water for your beer, and then put your wort right back into it. Add a stopper and a blow-off hose, and you're fermenting a full five gallons.
It's best to start with more water than you need and boil down, rather than boil and dilute.