In 1/4" you might be able to get away with buying whats called a "S&D" drill (Silver and Deming). For a 1", it should fit your chuck. You don't have a lot of power so just take it easy on it. I've drilled 1" + sized holes on a cheaper and smaller drill press and got by with it.
The 2" hole is tough for trying to drill though. Instead, I use a hole saw. You're only going through 1/4 plate so it should be no problem. Just peck at it with some cutting fluid brushed on.