If you're looking to make a career out of it, don't be in too big a rush to get multi engine time. Your first job(s) aren't likely to be in a multi engine airplane; you have time to get the rating. First, concentrate on the certificates and ratings that will get you employed and flying.
There's nothing wrong with getting a multi engine rating and a little multi experience, but even if you get your certificates in a multi engine airplane, you still have a relatively insignificant amount of time...not enough total experience to go get hired. You also have a great deal more expense getting through your certification. If you have two hundred fifty hours and half, or all of it is multi engine, so what? By the time you reach the VFR minimums for 135 at 500 hours total, half your time would be in a multi airplane. However, nobody is going to hire you into a multi at 500 hours for a VFR job...concentrate on getting useable time and experience.
As you gain more experience and get closer to having a significant enough total to be considered, your percentage of multi shrinks and dwindles, somewhat reducing the value of your expensive investment.
The wonderboy years are over, with a whole generation of people working into postions of significance with little or no experience. We're getting back to reality again. I got my first multi job with only 15 hours of total multi experience, but nearly 2,000 hours total time. Two years ago this was unheard of...folks wondered why one wasn't approaching captain status at their airline by then. That's not reality, and folks who experienced that or think that way don't understand reality. Today is reality, running on the typical ten year cycle.
Don't be in too big a rush to spend the almighty dollar on things that won't help you. Certainly it's good experience and not wasted in that respect, but you can spend less and get through certification faster and with less debt in a single engine airplane. You can get employed, and then work on the multi, for far less money than trying to do your certification and ratings in the multi. Something to think about.