When Should I start #2.
The truth of the matter is that unless you are gifted or very lucky, the second plane you own will also be a trainer. You need to be careful with the "2nd plane" threads. They're not usually talking about the numerical 2nd plane, but rather about the 2nd type of plane, the plane you'll graduate to after you've learned everything you can from your trainer and are bored with it, and that might be 3 planes down the road.
Therefore, to answer your question, you should be looking for a trainer-like plane, perhaps something a little more aerobatic, say with a semi-symetrical wing rather than flat bottom. But definitely a trainer-like plane.