I'm buying my first amp, my budget is $700 (US DOLLARS). I'm starting a band so I need it to be loud enough to play gigs. Currently I have a Marshall MG10CF and a Fender Strat. I play Hard Rock/Punk Rock, bands like Paramore, Green Day, The Runaways, AC/DC.

Used Peavey Classic 50 Watt
Used Maxon Tubescreamer
Used ISP Decimator in FX loop

Saves some of your cash for new tubes & a power supply.
I recently bought myself a Marshall JCM 900 with a Marshall 1960a cabinet. It works perfectly. I play a lot of punk music (Ramones, Sex Pistols, Blink-182) and it is perfect. But the amp is even perfect for heavy rock like Motley Crue. Although it does tend to cost a bit, my set i bought off eBay for 1200$ all up, it is well worth the money.
Although you might want to also look into a blues pedal of a tubescreamer to dirty up the clean channel, which is rather shit.
You've received some good suggestions, and to them I would add one more: Carvin.
"Maybe this world is another planet's hell?" - Aldous Huxley