As previously said, if you plan on having the MP3 player take some rough and tumble go for a flash based player. Lots of information around on these if you google them, basically, as already said, no moving parts so won't be a problem using them while jogging.
Personally, if I was to have a device for something which could cause it damage (any number of accidents could occur to a device if out running with it) I'd go for a cheap and chearful version which wouldn't cost the bank to replace.
When it comes to the wedding music, MP3 players can be a good way of getting playlists together that you actually want to play, but having a professional sound system is definatly worth going for (Also worth having the tracks at a higher rate than you would usually go for - with large/loud/professional speakers you should probably aim to rip them at the highest possible rate). Ask around some local venues, I'm sure some would happily allow you to hook everything up to the in-house system (some should have a pre set up outdoors system - I know most in Spain and Portugal do, I presume Italy would too) knowing they'd make on the bar/food takings.