If ever there was a twin made for this it’s the DA42, BUT, its not likely your best option.
I can’t imagine a fleet owner letting a student solo in a DA42 and expecting to keep his insurance.
If you buy the plane yourself, you will spend so much in insurance that you could have easily bought a DA40, built a couple hundred hours, and then swap it for about the same amount of cash.
You should try to price a DA40 purchase or lease with a guaranteed trade in deal on the 42 (lease deals are rare, but you could possibly find a dry lease if you know how to look). Cost out buying a used 40, and trading up. Cost out renting a 40 if one is available (glass 40’s don’t generally rent as many hours as basic trainers, so renting one is not so bad). Compare that cost to buying a 42 straight out of the gate and paying insurance if you can find it.
If you are doing this without insurance, you might be okay with it except your risks are high for personal injury and 50k or greater loss due to a simple boo boo. The insurance guys aren’t being careful for nothing, they know the likely outcome is at best a wheels up landing.
Lastly, it will be more fun and relaxing to just start with the simpler airplane, and you will fly more hours more quickly because of this. Same goes for the SR22 and their plans for students, even if the thing has the wheels locked down. You are just better off starting with a trainer. If you really want to roll off the hours, buy an older DA20 and park it on the ramp with no cover. That way, you waste no time on hangars and covers.