The small planes into Champaign-Urbana do indeed get cancelled and delayed, especially in winter. Faculty at the University of Illinois either tend to often plan to drive to ORD or IND for their travel or they frequently rent a car when a flight is cancelled in order to travel on the desired day. AFAIK Champaign is also served by DL from DTW, which IME is a better airport than ORD for winter travel as it tends to stay open and has sufficient capacity to handle its scheduled flights, even in bad weather. So DL from LAX, SFO, JFK or EWR with a connection in DTW would be another choice to consider. (Don't try to connect through Canada on SQ as this would probably require a visa since you would go through immigration and customs to enter Canada before going to the area for USA departures, which are almost all precleared by USA authorities in Canada.)

As a young student from Singapore DO NOT EVEN THINK OF RENTING A CAR AND DRIVING YOURSELF. You are not familiar with USA driving patterns and signage, even if you have a license in Singapore, and you are not experienced in driving in ice and snow. (You're young, but you might still be very jetlagged, given the excitement of travel to your new school.) Moreover, you are probably too young (under 25 for the major rental car agencies) to rent a car in the USA and even if you can find a company willing to give you a car, there will be an exorbitant surcharge for the insurance, in addition to the one-way rental surcharge.

Think about luggage in making your plans. Get your ticket in a way that the luggage can be checked through, ideally for a single fee (or free if you are a *A elite). Also think about how you will get your luggage from the airport baggage claim to the bus or whatever, and then from where the bus stops (probably at the student union in the center of campus for the university-operated bus service) to your new residence. Taking a taxi from the Champaign airport would be much easier if you will have a lot of stuff. Also verify that you can get keys to your new residence, probably a dorm room, at the time you will arrive and know exactly where you must go (office in another building?) and what the procedure is, for example will they ask for a small cash deposit or fee? What sort of ID will you need to show?

If you do opt for a public bus, be aware that there are some new long distance bus companies in the USA that operate service oriented toward young people, including free wifi during the trip. They tend to sell very cheap advanced purchase tickets on line. It's very different from using the old standards of Greyhound or Continental Trailways, which have the advantage of leaving from a real station rather than a street corner (with no facilities or shelter while you wait).

Enjoy Illinois! You can get a very good education there.