I'd be looking for a duplicated vacuum & power system, which no microlight or LSA has. After that, reasonably firm apparent longitudinal static stability - say 1lb/6kn or higher, and positive spiral stability.
A CT, or even an X'Air for example, would give the handling, and it would be easy to put a battery backed up electric AI and a second altimeter. A few - such as the Eurostar which has neutral spiral stability I'd be more concerned about. A C162 would be fine as well from the LSA category.
Certification requirements do require a few other things, such as a certified engine.
I've never seen anything in the serious technical discussion which discounts LSAs on stability criteria alone.
G