The ticket information will be sent back to Manitoba, so they'll find out about it, and then when you apply for an Ontario license the infraction will be transferred to your record here. Whether or not your rates go up depends on your insurance provider. (Are you still using insurance from Manitoba?)
Basically any speeding ticket can be used to raise your rates, but some insurance companies will forgive one or two tickets for 15 over the limit.
Setting a court date is a good idea. It gives you options. You can plea-bargain to a lesser speed, see if the officer shows up, or other things. If they'll be kind enough, you can even try to plead for a municipal by-law infraction, which results in no driving conviction. You can even call the Prosecutor's office in advance of the trial and arrange for a meeting.
Based on the fact that you're currently a student, I'd imagine you don't have a tremendous amount of free time on your hands, but if you really want to see if you can fight this all the way, start off by making a disclosure request, and check out this thread that was put together by one of our members. It's the most comprehensive effort by anyone to fight a ticket:
http://www.ontariohighwaytrafficact.com/topic1092.html
Neo333 did a lot of solid work on that one.
You have to decide what course of action is best for you. Good luck!