I am probably not the most qualified person to reply but I'll have a go.
From my limited view of the bizjet world (ie just started in it after a variety of flying) is that they (the employers) want someone who can think independantly as well as the nice stuff like fly an ILS. You'll probably need more hand flying skills than a bog standard airline pilot simply because you'll be going into VFR airports as well as the SID-STAR-ILS flying.
I dare say that some good quality turboprop time operating independantly with minimal support will be viewed more favourably at this stage than pampered jet/autopilot/autothrotte/auto every thing time.
Multi IFR time is invaluable. Get some good experience in your log book, you won't go wrong. Also, handling customers is another big plus. Being able to sort out fuel, catering and so on is a huge advantage.
You could try having a chat to the various bizjet operators around and see what they like to see in a log book.