You do not have the greatest deal. You plan to take on the most difficult job in the residential heating and air conditioning field. This knowledge takes a year of vocational study and several years of experience to respect the mistakes that can be made. You have taken away your safety line of having a contractor guarantee his equipment as anyone you contract with did not supply it. You want to find the supplier of the equipment to find out if the supplier will back the warrantee.
A contractor you find to do the work is going to have to tiptoe around the fact the equipment is something he would not or did not supply. He will have to follow all local codes as to installation or have the potential of being sued for helping out, so the savings you are looking at are small - the appliance parts you have are the smallest part of the cost of a complete installation by a knowledgeable contractor. The R-22 you have cannot be purchased legally without a license proving that the professional knows how not to pollute the atmosphere while using proper tools. An experienced contracting company has to pay for the overhead of an office, payroll, trucks and equipment that cost him about $50 per hour or more before he takes home his own pay.
Finding a handyman to attach up parts without proper licenses and experience can mean you can have a terrible installation and a ductwork system that can not handle a good piece of equipment to replace the improperly installed failed one. This is a difficult situation for you. It is similar to getting and engine and transmission for free and trying to get the rest of the car you hammer together licensed for the road.