Bithburysloth - As you have orthoses, they should be sorting out what your feet are doing (biomechanically) and now what you need is a pair of shoes which fit your feet and orthoses well and provide a stable platform for the inserts to do their job.
The medical professional who prescribed/designed your orthotics is the best person to advise what category of shoe you should be using as he/she will have designed the orthoses for a specific category, if not a particular style.
I would agree with Nick L that you should head to your local running store to try out some shoes with your orthoses. Although I'm not sure what you gain running barefoot or without the inserts if you're going to be using the inserts whenever you run.
Product-wise, the ProGrid Ride is the latet version of the Trigon Responsive, although you might also want to look at the ProGrid Echelon which is build on a straight, broad last, ideal for use with ortotics. Both of these are stable neutral andprovide a great platform for the orthotics. I use both of these styles mysef with my orthotics.
However, if you head to your local store you can try these and similar from other brands to find the best fit and feel for you.
I hope this information helps.