vibrations like that are usually caused by wheels that aren't balanced. try swapping your back wheels with your front ones, if it makes a difference then you know the wheels need balancing.
you could always take apart the area that rattles and stick silicone on all surfaces that touch each other, or even double sided sticky tape would work, or for a quick job just jam some paper inbetween the rattling parts. if 2 bits of platic are touching they will rattle when they vibrate. no big deal, certainly not a fiat only issue, every car i've ever owned had rattles.
all cars have problems, i admit some more than others, but to be honest the brava problems are mostly easy to fix and not serious. fiat dont deserve their reputation anymore, they've come a long way since the rust bucket days.
a rover with a k series engine will blow its head gasket once a year, any ford pre 1999 will rust away to nothing, many french cars have engine and electrical issues that make fiat look perfect (citroen airbag disease, renault random belt snaps, peugeot electrics on most models, need i say more).
if you want reliability and trouble free motoring, get a honda, nissan or toyota, everyone knows they beat anything from europe. they usually have crap interiors and look like they're designed for grandads, but thats life.
personally i think you'd enjoy life with a vw, for example the golf is a great car, i've worked on a few of them over the years and the build quality is tops, even the mark3 golf is still good. they handle wonderfully, the brakes are great, the interior is well put together, the engines are all good, gear change is lovely, i cant fault them really. if you go to china almost every car on the road is a vw, i was there is 2004 and 60% of the cars were vw jettas, i saw loads of taxis with over half a million kms on the clock, the highest i saw was over 800,000km (half a million miles). any car that can do that has to be good.