Ignition Override:
You will probably find that the handling characteristics are fairly intuitive and easy to get a handle on. V1 engine failures are a fairly simple exercise but there are a couple of considerations to nail the technique. First of all, directional control is easy, you just apply rudder to maintain directional control and then once airborne, hold that initial pressure until the Beta target appears. Once it does, centre the Beta target with fine tuning of the rudder pressure but don't rush to set the trim, because at this point, pitch should become your primary concern to ensure proper climb performance. The pitch control can be a bit tricky in the initial stages of the engine out takeoff as the flight control laws change. The general technique is to set the pitch at the initial target (around 12 degrees) and then fine tune it once the climb stabilizes a bit. There is a tendency for the pitch attitude to increase after it's initially set when the controls go into normal law, so keep an eye on that. Also, once you've got the attitude set, relax your grip on the stick to avoid "stirring the pot", a common error for new pilots on the FBW. Once you've got a good handle on the pitch and rudder, you can get the rudder trim set (which takes a few seconds so be patient) and then get the autopilot on. The autopilot handles the engine out very well once the trim is properly set.
As for complex procedures, have a look at the QRH in the Emergency Procedures (section 1.00) and also the associated FCOM bits regarding Emergency Electrical Config, and dual hydraulic failures. The fact that Airbus has created multi-phased Summary Checklists for these procedures points to their complexity. They are a nice guide to handling these situations from the start of the failure up to the end of the flight. These are the most complex ECAM / QRH procedures and should be studied thoroughly and briefed in detail before attempting them in the sim. Dualcouple is right, green and yellow hydraulics is the most complex because you lose the most systems. Plan on a flapless landing with a high pitch angle, no reversers and no nosewheel steering (among other complications). Smoke/Avionics Smoke is another complex checklist, but it does lead you to the most likely causes if followed correctly.
You're fortunate in that you're learning the airplane at a time when there's a ton of operational experience and the biggest potential "gotchas" have already been used in the development of the training. Much better than a decade ago when most of us left the check ride with more questions than answers! Still, it does take a few months of line experience to go from "What's it doing now?" to "Look, it's doing it again!" (This is all tongue in cheek, because while it used to be said alot, it's not as much these days now that we really understand the Airbus logic.)
Enjoy the airplane!
Jeff