WHAT TO WEAR
Waterproof textiles or leathers and an unlined oversuit? Both have their advantages, and many people have more than one option these days. The main problem with wearing unlined lightweight plastic waterproofs is that they don't breathe, and in certain conditions you can get as wet from the inside out as you would from the outside in were you not wearing them. If it's chilly and wet, they're fine, but ride in wet, mild weather or spend a lot of time at low speed or around town and you can end up a bit sweaty.
That aside, unlined waterproofs are generally cheap and easy to carry around when not being worn, and a good quality unlined one-piece suit with properly fastened cuffs and collar is about as waterproof as you can get on a bike. You also get to entertain passers-by as you struggle into it at the side of the road when the heavens open, hopping from one foot to the other as you try to get the suit on quickly without taking your boots off.
Textile clothing with a waterproof, breathable lining such as Gore-Tex has many advantages over the leathers and oversuit option. For a start the jackets and trousers are far more versatile, with removable linings, body armour, pockets and multi-adjustments. Providing the breathable membrane works as it should, you're less likely to get too sweaty underneath - although there are limits to how much body heat a textile jacket can deal with, so don't expect miracles on a hot day.