JT has some good ideas. Here are some other thoughts...
You can maybe do this yourself, depending on your experience and abilities. From how you describe it, you might be better off with a penninsula instead of an "island". I think I have a similar situation. I have a galley kitchen which has cabinets on the left wall, sink straight ahead and cabinets on the right wall with a passthrough above the counter. I will make a penninsula that comes out from the sink side to the right. This will leave room to walk by into the dining area. If you use a penninsula instead of an island then you can use a wooden butcher block counter top that is just butted up to your existing counter. This is really the only material that pretty much can be put next to any other and still look good.
Some things you have to consider if you remove the entire wall: 1. You will have to patch the ceiling where the wall left a big ugly gap. This can be very difficult to have it look good, especially if you have textured ceilings. 2. You will have to be careful not to cut through any electric wires that are going through the wall and maybe move, or eliminate outlets that are in the wall. 3. You should be 100% certain that you don't have any plumbing or heat ducts/pipes running through the wall. 4. You will need to try to patch the big gaping wound in the floor where the wall was. 5. You will need to patch where the wall removal left a big gaping wound in your side walls.
There will almost always be some other unforseen circumstance come up while you are doing this. If not done well, this alteration could end up decreasing the value of your home. If done well, it will increase the value. I don't mean to sound too negative. This job can be done by a do-it-yourselfer, but care must be taken in assesing whether you are up to the tasks, since it is major surgery.
Other options: You might want to just make a "passthrough" in that wall. This is basically a big hole you cut through the wall. You can mount a counter on it and have stools on the other side. This would eliminate most of the issues I listed above.
As always, you should make sure that you have any required permits and inspections etc..