Big 3 or new battery?

[Xjeff 10+ year member]

So I'm buying my girlfriend a sub and amp for her car. I figure with the combo her lights will be dimming on the stock wiring she has I don't have money to buy a new battery and big 3 for her car right now so which would be a better option? I know I can buy the stuff for big 3 for about $45-$50 and a new battery would be probably $150 but would a new battery give the amp more juice than the big with with stock battery? I plan on getting both down the road. Which would be best to upgrade first?

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[gckless 5,000+ posts]

Both, big 3 first. What size amp?