Connecting a 120V/30A variac to a 240V circuit
Connect your 120 V variac to your 120 V circuit. It will only draw current determined by its load, plus a bit of magnetising current.
The fact that the variac is rated to 30 A means it will stay nice and cool when it's supplying the maximum 15 A at 120 V output that your circuit can deliver.
Your supply/variac combo will then be rated like this
output voltage 0 to 60 V, maximum output current 30 A (variac limited)
output voltage 60 to 120 V, maximum power output 1800 watts (supply limited)
Use it like this for now, to discover how actually use your variable testing / prototyping supply. You might find it's adequate. If later on you really need that top right-hand corner above 60 V filling in all the way to 30 A, then you can invest in a 240 V to 120 V auto-transformer to beef up your supply.
Note that this variac will not be giving you isolation, it's usually isolation that's the number one priority for doing testing / prototyping work. You might want that 240 V to 120 V transformer anyway, and invest a bit more on making it a proper isolating transformer, rather than using a cheaper, non-isolating, autotransformer.
You may find that a 30 A rated variac trips your breakers from time to time when powering up on a 15 A circuit, maybe more often than you would like. All transformers have the capability to draw significantly more than their rated maximum current for a few cycles, if powered on at zero crossing, which is the worst case point in the mains cycle. If it just happens from time to time, then it's called nuisance tripping, and we can live with it. If it happens too often, then there are ways to deal with it. A time-delay breaker is perhaps the easiest solution, one that's specified to ride out a few cycles of overload without tripping. But there are electronic ways to turn on the load at peak mains voltage, which results in no power-on transient, or soft-start it using other methods.