You need to work out what you need first, so need to know detailed specs of what you have, I find a popping into my LBS can supply this info:-
front shifter - is existing double and triple compatible
front mech - as above
bottom bracket - will it work with triple re chainlines etc
frame - will you have clearance at chainstay for what you need
alternatively could you fit a new longer cage rear mech and a wider ratio cassette? You'll probably have a max range at the back of 11-27 with a road mech. So 34x27 gives you a low of 33 gear inches. A 30x27 would change that to 29 inches, whereas a 34x34 would give a low of 26 inches. With the triple you'll get closer ratios in each front ring, most people seem to ride in the middle ring and treat inner and outer as overdrives. With the compact and wide range cassette you'll have bigger gaps between gears and may need more front changes.
So it depends on how you ride, if you like to maintain a cadence and adjust gears to accomodate then triple and close is better. If you don't mind varying your cadence then you may prefer compact and wide. Some people don't like long cage rear deraillers and don't like big cogs at the back, for aesthetic reasons. Personally that doesn't bother me, I could quite happily tool around on 50/34 with an 11/12-34 at the rear. Staying in the 50t ring most of the time, 40-120 gear inches and treating the inner ring as a bail out for hills. But it does mean closer to 10 inch gaps between gears rather than the 5-6 inch gaps you'd have with a triple.
I'm sure I've missed some bits and other, more knowledgeable folks can fill in the gaps.