What people have done in the past.
Initial twin endorsement was on a Baron, which was flown VFR, Special VFR, and private positioning NVFR for a few years before the I Rating was done. The initial NVFR Twin was converted from the Single in an old Apache. Then later the MECIR was done in an Aztec while on leave. Hardly ever flew an Aztec again as I was still on the Baron. Had over 2000 on singles before the Twins, and about 4000 VFR before the I Rating.
Realise things have changed now, with loans taken out or sponsored, money up front to get the rating with glass and GPS Approach experience etc, just to get started. But with a bare licence and low time, some things never change. If you have the money, do it in an aircraft you like, and think you will use later, and get familiar with it, and build time. Otherwise, together with the previous good advice from the other posters, my other suggestion was do it cheaply (but thoroughly) in whats available, and save cash for the inevitable lean times while cracking that first "being in the right place at the right time" experience. It may be in the right seat of a turbine multi-crew, so the type you trained on wont matter anyway.