A DIY approach may seem cost-effective, but it may be a better idea to leave it to the professionals.
Depending on where you live, you may need a permit to install a new unit. A professional in your area already knows the ins and outs of this process. Adding refrigerant to your AC unit or removing an old unit that has refrigerant inside may also require an EPA certification. To obtain this sort of certification, you must pass an exam and pay a fee, whereas a technician is already certified.
You could also end up paying more over the long run by installing the system yourself. If ductwork is not properly sealed and insulated, it greatly reduces your system's efficiency and you could see massive spikes in your energy bills.
Installing the system yourself may also void the warranty, as most require units to be installed by licensed technicians.