"I can get the appliances I want quickly from a company that does not provide installation service (or haul away old appliances.)"

Will it deliver the appliances? Does it deliver to the curb, to the door, inside, up stairs, into your kitchen?

"Or I can go with a local company that does installation/haul away but it may be months before the appliances are delivered."

When do you need the appliances? What's the difference in price between the non-installation company and the local company?