1 bucket
1 bottle bucket
1 capper and bottles OR plastic brown liter bottles
1 Hydrometer
1 4 or 5 gallon brew pot
1 container of sanitizer
1 airlock
I get away brewing with the above components all the time. There are additions that make life easier and enhance your capabilities, strainer, mash tun, hop bags, chillers, mill, etc... but with the above equipment, you could brew 5 gallons of beer easily, and safely. You would need to brew extract and concentrate your boil, then add the additional water prior to pitching yeast but this is frequent with extract kits and I still do it myself if I don't feel like getting the mill out and mashing grains, tagging some hours onto my brew day.
There is another option you may want to look into given your situation and that is Mr. Beer. Some frown on MB and I will admit it is almost too easy, but a lot of brewers on here will tell you they still have their 2 gallon brown keg around somewhere and that's where they started, myself being one of them.. Hell when I go stock up on regular ingredients I generally pickup a MB refill or two just for the convenience (currently drinking their version of Oktoberfest and it's not bad at all, I've enjoyed it!).
A standard MB kit will get you their low end ale ingredients (prehopped extract, a booster pack, yeast, and a sanitation packet), you'll get the mr. beer keg which not only acts as a fermentation chamber, it acts as a bottle bucket as well. If you upgrade you get the brown liter bottles as well. Each refill pack is 10-20 dollars and produces 2 gallons of beer, you can order the entire kit to get you started for 25-30 bucks on Amazon, free shipping (I know, I just bought my buddy one for his birthday).
Just another option though I heavily recommend you double the time windows they give. If it says 2 weeks primary then bottle, give it 4. If it says 1 week in the bottle before drinking, give it 2+. Bad part about these kits or most any, they tend to push you through your beer before it has a chance to be really good.
Best of luck!