I'm with Obed and Egon.
The more of the tree that you have to work with, the easier and faster it is to get the stump out. While leaving the trunk as tall as possible is better then cutting it short, leaving the entire tree intact is even better!!! I've taken out tens of thousands of trees on my place with my backhoe and dozer.
I can get the biggest tree out fairly quickly with either machine, but every stump is a struggle. Some have tap roots, others have several massive roots that go out just under the surface.
And then there are those that are in dirt that's more like concrete. Soil conditions play a HUGE part in how easily a tree will go over. In the wet months, I can push over most trees with one try with my dozer. It's a Case 1550 that's comparable to a Cat D6 or Deere 850. It weighs 40,000 pounds and has 169hp. It's a beast, but when the soil is dry, the size of tree that it can push over goes way down. I've snapped off trees that just a month earlier would have pushed over easily.
Ideally, an excavator is the best choice for tree removal. They are sized in metric tonnes. A 12 tonne machine will get the job done, but it's on the small side. 15 to 16 tonne are very common and a much better choice. They weigh around 35,000 pounds and are easily transported without permits. Same with the 20 tonne machines, but they are allot more money to run. Obviously, the bigger the machine, the more power it will have and the faster it will take out the trees. A 20 tonne machine will pretty much be able to pull out and stack most anything that you have. Anything bigger is getting towards the overkill side of things and probably too expensive to deal with.
While a dozer will get the job done, I've found that I can take out the larger trees faster with my backhoe then I can with the dozer. I can dig around the roots and push it over with less digging then the dozer requires. Digging out roots with the dozer blade, then building a ramp to get up high enough for the leverage to push over a big tree takes allot of dirt to be moved around. It's just not the best choice for tree removal.
With just an acre of land to mess with, the excavator can pick up and stack the wood in a burn pile that will be very clean. It has to have a thumb on it, but that's a given if they are doing land clearing. The dozer, even with a rake, will push dirt with the trees. Dirt doesn't burn, and even worse, it quickly adds up to a very large mound at the burn pile.
I now have a grapple on by loader that is perfect for picking up the trees and carrying them to the burn pile. It's fast and clean.
The dozer is best for cleaning up the area after everything is done. Since it's just an acre, your tractor could do just as good a job with a little more time.
If it was me, and I was going to hire it out, I'd start interviewing guys with excavators. I'd talk to as many as I could find. I'd want to know how old their machine is, what they charge and when they could start. If they are out of work and real hungry, I'd be nervous about hiring them. The guy who is busy is keeping clients happy and there's probably a good reason he's working while the other guy isn't. Cheaper isn't always the less expensive way to go.
When hiring an operator, be sure to have his rate written down and agreed to before hand. Some will charge by the hour, others by the job. Either way can work out well for you, but you can also be taken advantage of either way. If it's by the job, it's going to be high in order to cover unexpected suprises. For a small job like yours, it shouldn't be too bad. If by the hour, you have to make sure you are not being charged for hours not worked, or hours fixing the equipement.
Older equipment allows a guy to operate for less money because the machine should be paid for, or it cost less to buy. It also means that it will break down more often and down time can become a real issue. Newer equipment is very expensive, but it gets the job done and it shows that the owner of it is more prone to buy the better machine for his business. I've never run into problems with guys who have new or newer machines, but always have problems with guys who have old, worn out, machines. How they take care of their equipment is also a big factor, and a good indicator of how your job will turn out.
Ask for references and go to the job they are currently working on. Look to see how clean it is and find out if the references are happy.
Good luck,
Eddie