BG I agree, that the smaller boxes do their things better, but the versatility that you get from a unit like a multi fx board is better... IMHO... You dont have to fiddle with buttons to get to a completely different sound : distortion, overdrive chrus modulation etc... and the units are infinitely easier to transport except if you have a dedicated pedal board...
Now I decided to go for a more expensive amp and FX modeling processor and it is worth every cent... I have the fersatility to sound like any of my heros (that is the sound not my playing...) and the fact that I can put it straight into a PA system makes it even better when travelling.
I must say though that It will never be better than the real deal it will only ever get so close that you will not be able to hear the difference...
I have the Tonelab SE wich sells for around $400... you can go for something cheaper though seeing that you are only strating to fiddle with FX... Get a Korg PX4D Pandora as Allthumbs suggested they are great little machines for the price... but dont listen to us go to a shop and play with the different ones they have available...
All you have to do is be aware of everything we tell you when playing them, and then ultimately make your own descision.