The reason I ask is because when I was trying to trim the aircraft for straight and level I think I was relying too much on the VSI and not quite trusting the AH, should I be looking for straight wings on the AH first and then confirming the 0 VSI reading, or is it the case that at many power settings the AH is in fact not level for straight level flight, and so I should be focussing more on the VSI?
Focusing is the wrong method here. You should never, ever focus on one instrument for any single piece of information. This is what leads to pilots being surprised by a stall, spin, or spiral descent during the initial stages of instrument training.
The most useful phrase in any type of flying is the good old "power plus attitude equals performance" and remembering this will serve you well as you transition into instrument flying. Your VSI could indicate 0 fpm but, as TangoAlphad pointed out, your pitch attitude could be anywhere depending on the power setting.
Ask your instructor about the T-Scan. They should tell you that it starts by looking at the attitude indicator and moving about the instrument panel in a methodical method depending on what you're doing. You'll eventually find that this method is too tiring for anything more than a single training session and you will develop your own method in time, but the T-Scan does drive home the importance of combining sources of information to complete your mental picture.
For example, when climbing on a specific heading, the most important sources of information are pitch, airspeed, and heading. So you'll start the scan at the artificial horizon to set your pitch, look across to the airspeed indicator and ensure you're climbing at the required airspeed once you've set the power. Then look back to the artificial horizon to make sure you're still flying the correct pitch angle, before looking down to the directional gyro to ensure you're flying the proper heading. You'll then look back to the artificial horizon and start the process over.
After a couple scans, you'll include the altimeter and VSI in your scan, using the same method (e.g., AH - ALT - AH - VSI - AH). Every now and again you'll also include the engine instruments.
As you approach the target altitude, you'll include the altimeter more often in your scan than, say, the airspeed indicator. Once you're level, you'll readjust the pitch and power, and will rescan for what is now important during level flight (attitude, altitude, and heading).
Like I said, it is tiring moving your eyes, but the important thing is learning what information to look at when and, as you learn your aircraft and how it performs with various power and attitude settings, you'll learn to rely less and less on the T-Scan and more on your individual scan pattern.
Good luck!