Arduino Power - DC adapter
Don't worry about the current limit. The board will only draw what it needs. The spec is telling you that the board can draw as much as 1 amp, so in general the power supply should be able to supply that – more is no problem, but less could be if you have a lot of devices attached to the board that are drawing power as well.

As is pointed out in the comment above the higher the input voltage the more power the on-board regulator will need to dissipate (as heat). If you are using the barrel jack (which you should if you aren't providing power through an external regulator or other stable source) there is a diode (D1 in the reference design) in the input path and the MC33269D-5.0 regulator is spec'd with a max dropout voltage of 1.25 V so you will need an input voltage of at least 6.95 V (assuming a 0.7 V drop across the diode).