I'm not sure how much MORE an oral surgeon would cost, but when I had my wisdom teeth out I paid $100 per tooth. Therefore, all four teeth -- $400. Anesthesia was included in this price. That was fourteen years ago; probably you can expect a slightly higher price, but maybe not. It's also impossible to give prices for this kind of stuff -- dentists have different rates, local economy plays a part, etc.
I'd personally suggest an oral surgeon, though I am quite sure your dentist is capable.
I'd also request a Valium IV drip, not simply Valium tablets administered the night before and prior to surgery. The IV drip, combined with nitrous oxide is marvelous. And of course the local anesthetic, which is pretty much mandatory.
The "pressure" you will feel is nothing. Some tugging sensations. With the Valium IV drip and laughing gas and anesthetic, you won't know what the heck is going on. I drifted off and felt fantastic. I was disappointed when they gave me oxygen and brought me out of it! It seemed the whole procedure took two minutes, but it lasted about an hour.
Keep in mind that folks who post about complications or pain or bad dentistry are in the minority -- and these folks come to message boards to seek support, as well they should. But MOST extractions are uncomplicated, painless and recovery is swift if you follow the proper after-care procedures the dentist will give to you.
This is almost certainly going to be much LESS of a big deal than you think. I wouldn't worry one bit about it. Just do request a Valium IV drip. If your dentist will not or cannot provide that, consult an oral surgeon.