Talk to your HVAC guy first. Years ago, I was offered a screaming deal on a furnace. I got bids for having it installed and they weren't any different than having the HVAC install a new unit that they provided themselves.
It's very unlikely that you could install an AC unit yourself. My electrician will install and wire heat for a lot less that the HVAC guys, but he can't do AC. You need specialized guages and a licence to handle coolant.
It's very possible that your HVAC guy can buy the unit cheaper than you can.
I've done some serious shopping and haven't found AC or heat pumps at any sort of price that made me sit up and flap my front flippers and bark.
One suggestion, though. There are little one man HVAC companies and I find them to be about 1/2 the cost of the big guys who advertise in the Yellow Pages and on TV.