Unless your goal is to drop parachuters, fly oil pipeline patrol, or work for a FedEx feeder flying Caravans, you are probably going to need multi engine time. How much you need depends on the supply/demand hiring cycles in the industry. When there are few jobs and a surplus of pilots, the first thing employers do is raise the flight time requirements to apply. The second thing they do is raise the amount of multi engine time you need. The industry benchmark for the last 10 or so years has been around 200 hours. But a good rule of thumb is this...you can never have too much multi engine time.
When you are a new pilot trying to break into your first real flying job, say with 1200 hours total time, you are a literal needle in a haystack. What you need most is something that will make you stand out from the crowd. A bachelor's degree is highly recommended, but many people already have that. You need something more. That something is multi engine time.
When a prospective employer is shuffling through 500 resumes (all having 1000 to 1500 hours) and yours has 1200 total time with 950 hours multi engine time, your resume will go to the top of the stack. Unless you are a convicted felon, you are going to get called for an interview.
Not only are employers looking for a bare minimum of 200 multi engine hours, they also want it to be recent experience. Again, if you plan on flying for the airlines or corporate, don't treat multi engine time as an after thought. Make it your primary focus. "So how do I do that?" you ask. Easy! Find a flight school that puts you in a twin as soon as possible, and then keeps you there.
Characteristics of a good multi engine flight school...
Here is a good course progression that some successful flight schools use.
Private ASEL (Airplane Single Engine Land)
Private AMEL add-on rating (Airplane Multi Engine Land)
Instrument AMEL
Time build in a multi engine until you have enough time for your commercial rating.
Commercial AMEL
Commercial ASEL add-on
MEI
CFI/CFII ASEL add-on ratings
Instruct as an MEI and build multi engine time.
Benefits of attending a good multi engine flight school...
Here are the benefits of a school that follows a course progression similar to this.
You become very comfortable flying a twin. (Very important)
You build lots of twin time. (also very important)
The school you chose uses primarily multi engine airplanes, so guess what...they will use you as an MEI.
Your resume will not only have lots of Multi engine time, it will also be current multi engine time.
When you transition to your first jet you will be more prepared.
Let me spend a paragraph on clarifying what I said in number 5. I'm not saying transitioning to a jet will be easy. It will be challenging. You are a very rare person indeed if going from a 120 knot airplane to a 400 knot airplane does not make your head spin. Multi engine flight training is serious business. The majority of your training involves learning what to do when one of the two engines stops turning. The instructors at the flight school I attended used to joke that they had more single engine time in a Beech Duchess than they had in a Cessna 172. It's true. As an MEI, flying on one engine becomes second nature. It is those people, in my experience, who have the least difficulty when transitioning to a jet. They already have the "flying on one engine" concept down pat. They can then focus their attention on getting accustomed to the blazing speed. And, in general, they are the easiest to train. That is why their resume's go to the top of the stack.
Let's review. First, since you'll most likely be flying a multi engine airplane the majority of your career, why not start off learning to fly one right away. Schools that specialize in multi engine training usually can offer it for a competitive price. Second, schools that primarily use multi engine airplanes will need MEI's and will hire you on course completion. Third, you will build tons of current multi time which will make your resume stand out. If your resume stands out you'll most likely get the interview. If and when you get the job, you'll most likely be more prepared for the intense training that you will be required to undergo.