You'd need a medium cage derailleur, or in Shimano parlance, "GS".

Here's why:

Your chain needs to be long enough to wrap around your biggest chainring and biggest cog. When you shift out of that combo, though, your chain would go slack if it wasn't for the spring-loaded cage of your rear derailleur. Rear derailleurs are sized by their ability to take up chain slack, and that ability is measured by a derailleur's "wrap capacity". To calculate your required wrap capacity:

1) Subtract the number of teeth on your smallest cog from the number of teeth on your biggest cog.
2) Subtract the number of teeth on your small chainring from the number of teeth on the large ring.
3) Add those two numbers together.

In your case, assuming you're running a compact double crankset: (32-11) + (50-34) = 37

So you need a derailleur that has a 37-tooth wrap capacity and can handle a 32-tooth cog. It just so happens that the Ultegra RD-6800-GS medium cage derailleur is rated for EXACTLY those specs.

As for the chain length, you'll have to measure that on the bike. catgita described one common method of doing so. We can't tell you a number of links because we don't know how long your bike's chainstays are. (And even if we did, it's probably easier to size it on the bike than to do the math.)