battery dead

So me and my roommate just got an '84 CJ7 with a Ford inline 6 300 cubic inches engine. Unfortunately, the battery dies the second we cut the engine. We think it's an alternator problem, but not 100% sure. If so, what type of alternator do we need? Thanks!

Hello, For the past couple of months, my jeep has been on and off, having problems starting up fully - it will sputter and I have to keep pressing the gas until it "catches" - it typically happens after I have been driving around all day (it never happens when I start it in the morning). I...