Im in a similar situation, I just bought a larger kettle so I can move to 5 gallon BIAB batches and choose that because 5 gallons seems to be the standard size. Most recipes are based on 5 gallons, and 5 gallon carboys are way easier to find (and normally cheaper) than 3 gallon ones. That being said Im still looking out for some 3 gallon carboys for a good deal, just to have around.
Upgrade wise, you will need a larger kettle. I just got an 8 gallon which is a little on the small side, but it was a GREAT deal, $40 used from a former brewer vs >$100 for the plain jane 10 gallon at the LHBS
If you are brewing on your stove top, you may or may not have enough heat to bring 3-5 gallons to a boil, my stove struggled to bring 2 gallons to a moderate boil, YMMV
You will also want to invest in a wort chiller, ice bath in the kitchen sink works well for 1 gallon batches, is tolerable for 2 gallon batches, but for 3-5 gallons you will want a chiller just to save an hour of rocking the kettle in the ice bath and stirring the wort to drop temps significantly.
Lastly which should go without saying you will need a new, larger fermentor unless you plan to split your batches into multiple 1 gallon carboys.
Like they say, it takes the same amount of time to brew one gallon as it does 10, so why not go big!