The key to success or failure of any contract is the Statement of Work (SOW) placed in the Request for Proposal (RFP). The SOW will specify EXACTLY what you want a potential contractor to accomplish.
In your case, you would need to include such things as:
Specific responsibilities (both yours and the contractors);
Specific types of systems and software to be supported;
Numbers of users / systems to be supported;
Locations where support will be required;
Times of day and days of week when support will be required (24 hrs a day / 7 days a week, 9 to 5 / Monday through Friday, etc.);
Will support be required on holidays;
Required response times (i.e. tech on site within X hours of being called, etc.);
What will happen if you upgrade / add / change hardware and/or software after the contract is started;
Any special requirements that might be imposed on the contractor for access to your site (i.e. things like identification limitations - all techs must wear ID badges; physicallimitations - all techs must be physically capable of walking up 10 flights of stairs because there are no elevators; cultural limitions - sex, religion, etc.);
This list is by no means all inclusive.
You must strike the right balance between being too general (a contractor may have a legal right to refuse to do work, or charge more for work than was agreed on, because the contract was not specific enough), and being too specific (the contract may be so specific that no contractor can acomplsih everything being asked).
I would suggest if at all possible to have a legal professional look at your SOW to ensure that everything you ask to be done is legally enforceable. It does nobody any good to have a signed contract if one or more provisions are against the law or not legally defensible.
Good Luck.