The suits that the Olympic swimmers wear, are by and large the Speedo Fastskin suits, they come in a variety of styles, including one that is called a "bodysuit": long arms and long legs like a full wetsuit.
It provides no insulation or bouyancy and the donning process can take time (about 3x longer than putting on a full wetsuit). They work great for bodysurfing, but I prefer insulation for freediving, so I wear a wetsuit. But that would give you almost full body protection (the only thing exposed would be your hands, feet, neck and head), while still being very unrestrictive, lightweight and not much hotter than being lightly dressed (people wear shorter versions all the time in triathlons).
The suits are however pretty fragile, and typically last 10-12 uses (or less depending on how hard you used them) before needing replacement (I know this since I was part of the team that tested them for Speedo prior to the 2000 Olympics when they were unveiled: typically every swimmer had a new suit for every single race they had to swim during the Olympics, this maximized the effectiveness of the suit design, and eliminated the chance of "equipment failure" during a race. I managed to destroy a body suit in a single wear by wearing it bodysurfing for a whole day in Hawaii prior to everyones departure for Sidney). A full body suit will run you $300-$400 US.
The "grease" used by channel and open water swimmers is Lanolin. It gives a bit of insulation, eases chafing, and gives you topical protection from the "little beasties" as well. As far as getting it for yourself, ask around in the drug stores.
One thing that I found useful to keep me from getting stung by jellyfish, man-o-war and "sea lice" during my time as an ocean lifeguard in Florida in the early 90's was to use a sunscreen like Bullfrog or Aloe Gator. These sunscreens leave a slight chemical film on the skin that seems to make it harder for the stinging cells to attach to the skin. I used it alot, and while co-workers would get stung while on rescues using our "issued sunscreen" I never had any problems while using either of the sunscreens I mentioned above...... And the sunscreens are invisible...much more attractive than greasing up with lanolin.
And of course peeing on the stings does help take some of the "bite" out of it quickly by helping to break down the protiens in the stinging cells.....
