While the left hand gets busy creating the chord, the right hand gets busy doing the picking or strumming. The rhythmic strumming is often the most difficult part to master.
Most people choose an electric guitar while they are learning.
That way you can practice quietly without an amp, until you become a better player. How long it takes to get good at playing the guitar, depends on how much you practice. You should be able to pick up basic chords and strumming patterns within three to six weeks. Here are some resources you can use to buy and play the guitar. The Complete Idiot's Guide to Playing the Guitar.