Reversing direction of a 115v ac motor using Arduino
Assuming it's a "universal motor" which is the normal type of brushed motor running on AC, it will run equally well on AC or DC of either polarity, but always in the same direction. (As Olin says, the AC supply reverses polarity 100 or 120 times per second already. So, simply reversing live and neutral will not reverse the motor.

The trick to reversing these; and what sets them apart as more flexible than a permanent magnet motor, is that there are two windings : one on the rotor, and one fixed to the motor frame called the field winding. To reverse it, you need to reverse the connections to the field winding OR the rotor, BUT NOT BOTH.

If it is described as a reversible motor, these windings will be separately available as 4 external connections, possibly linked together, but in a way that you can disconnect one winding and connect it the other way round.
It's easy to identify the field winding : it has higher resistance and consumes much less power, maybe 10% of the total. The rotor winding goes to the brushes.

At which point a photo of the connection box is probably useful.

But assuming this is true so far, you can reverse the connections to one winding (usually the field winding which consumes less power) and test that the motor runs backwards - no circuitry needed so far. 

Alternatively, the rotor winding may be accessible via screw terminals on the brushes.

Then to switch between forward and reverse you need something like a DPDT switch (hand operated!) or relay (remote operated) to reverse these connections on demand. It may be better to stop the motor, reverse it, then restart, to prevent extreme mechanical stresses and current surges.

As for your other question : the 1 amp current is generally the current at rated load :you can bank on the starting current being much higher (easily 5x, maybe 10x as much). To estimate it, measure the DC resistance of the motor - say 11 ohms - and divide 110 (or 230) by it (for 10A start current). This is also the "stall current" which the motor will draw if you stall it while powered. A "motor rated" breaker will allow stall current briefly, but trip if the current persists for long.