Ted and Felix just bought twins so they might be able to shed more light on the subject.
Gee, Mari, how'd you know I'd come and chime in?
I was something on the fast track since I knew I wanted a twin from day 1 of flying. When I got to fly the Aztec (that I now own) at 11 hours TT, that just solidified the deal. I was told by insurance companies not to call back until I had 200 TT, they just wouldn't even talk to me.
I did about 160 hours in 172/PA-28 aircraft, and got my private and instrument ratings in those. After that, I joined an opportunity to start flying a Mooney M20F. I wanted to get some more complex time, and I also wanted time flying a faster plane. I've put about 70 hours or so in the Mooney at this point, and just past 250 TT on Sunday. I do believe that having the Mooney time plus the instrument rating is what made this doable for me from an insurance standpoint considering my otherwise low hours.
When I bought the Aztec around New Years, I had I think 225 TT (although no MEL) and got insurance at what I considered to be a reasonable rate, with the requirements of 25 hours of dual (of which 10 needed to be actual or simulated instrument time) and, obviously, getting my MEL. At this point I have 12 hours in the plane, and should be going for my MEL soon. I decided I was going to wait until I had greater than 250 TT so that I could go straight to the CP-AMEL-IA anyway, but I want to do CP-ASEL-IA in the Mooney first. So, at 225 TT with about 50 complex and a PP-ASEL-IA I became insurable in a piston twin with pretty reasonable checkout requirements.
One guy I know has been flying for 3 years, and he bought a Columbia 400 somewhere along the line, and then bought a Meridian. I don't know how many hours he has or what he had to do to get to it, but it is possible in a short period of time.
I also have a friend who, without an instrument rating, managed to get a SIC position in a Pilatus part time. That really came down to knowing the right people in her case, but it is doable.
I'm not sure what your ultimate goal is. My ultimate goal is to be able to fly (most likely not on my own dollar) cabin class piston and turbine twins (including pressurized) as a side gig for fun (not full time, I have a day job already), and then fly my own plane for personal missions. So given that, the progression I've been doing is as follows (with examples):
Fixed gear trainer (172/PA-28) -> Complex single (Mooney) -> Standard Piston Twin (Aztec) -> Cabin class piston twin (Navajo) -> Cabin class turbine twin (Cheyenne)
As much as possible, I also want to try to get time in my log book when possible in the bigger planes, since that will help make me more insurable. Also, getting something like some 421 time (pressurized cabin class piston twin) in between Navajo and Cheyenne time is probably good. At this point, though, getting time in the bigger planes is pretty much down to me knowing the right people and being ready to jump at opportunities to fly.
Also, I am planning on getting all my instructor ratings (CFI/CFII/MEI), but that is mostly because I want to teach people, and people seem to want me to teach them.