What kind of bike should I rent?
Quite a few different bikes there, but seeing as it is based in london, i assume you will be using the bike in mostly urban and city landscapes. My personal opinion would be to go with one of the many "Hybrid" bikes listed. Like one of the flat bar road bikes. If you go full road bike, you will be in "attack" position the entire tire and i imagine you would be more comfortable in an upright position where you can take in the scenery as well.

One thing to look into is what sort of insurance or theft policies are there? Parts of London could be a sketchy place to leave a bike so i would be sure you know the rules and liabilities involved with renting someone's bike. Also would be smart to inquire about repair services or rules if you were to get a flat or other issues.

Next, as others have mentioned, match whatever bike you choose with the type and length of riding you intend to do. A cruiser may be super comfortable for short jaunts around the block, but if you plan to put a lot of miles in, the comfort will loose it's bonus to expending extra effort.  

Also, i would avoid an older model being new to bikes. You will likely want a full range of gears and easy to use simple components like trigger shifters.