I'm a highway engineer, so you can blame me. However, I've only been doing this for 3 years and haven't been very involved in Right of Way issues.
I don't know what state you're in, I'm sure your state has a slightly different process than Pennsylvania.
What everyone else is saying is correct. You don't want to take the first offer the DOT gives you. In PA, you can get about two or three counter-bids, and then eventually they will get tired of dealing with you and start the eminent domain condemnation process. That is where things start getting bad for you. So don't resist too hard!
It might be difficult to work with the contractor to 'get other projects around the house' done, but you might talk with the equipment operator and see if a few cases of beer or a hundred bucks might help the process. I'd still doubt it though. The contractor or a demoliton/clearing subcontractor doesn't want to get caught with their men and equipment digging up your septic field when the state inspector comes by! Don't forget these men probably get paid upwards of $30-35 an hour, so a pan of brownies probably won't cut it!
Do you know where your property corners are? Are there markers at each one? If a crew of surveyors has already come through with their equipment, they may have either located the existing markers or set new ones. Do you have a plat of your property? That is a drawing with surveyor's notes on it, which should show where your property ends, and where the state's right of way begins. In rural areas, this may be referenced from the centerline of the road, which will make things easy for you, you just get out there with a tape measure and firugre out how far the right of way extends.
Do you have any easements along the edge of your property for utilities or any sort of access? Most likely, if you've got a row of electric poles on your side of the road, those poles will need to be moved further onto 'your' property too. (Did you really think it was yours?) Same with water, sewer, gas lines too.
In addition to whatever width the state wants to take for the road, there may be issues with stormwater. You may really hit the jackpot

, and get a stormwater management pond in your front yard! Some states use 'dry' ponds, they stay dry and ugly until you get a storm. Some states use 'wet' ponds, they stay wet (or at least squishy) all the time. Either way, less property for you.
As for your pine trees, you first need to determine if they're on your property or on the state's. If they're the state's, you're out of luck. If they're on your side of the line, you can take pictures and plead your case with the state's R/W guy. If they're unique, particularly decorative, extra large, or are the only windbreak on your property, you may be able to get a little more money for replacement of the trees.
You can also see if any of the right of way they want to buy from you could instead be either a temporary or permanent easement. Temporary construction easements will revert back to you once the job is completed, a permanent easement will still be your property, but you will be restricted in what you can do with it. Things like an 'occasional flowage easement' for storm flooding in low-lying areas are places you wouldn't build on anyhow, but you could still use it to graze animals on the other 363 days out of the year. Keep in mind whether you would still be paying taxes on these easements, and how restrictive the easement is, before agreeing to this.
Once the project starts, you will want to talk with either the general contractor, or the demoliton/clearing contractor (the name on the bulldozers). Normally any material that they're getting paid to remove, becomes the contractor's property. Sometimes the contractor has a way to get money for the material, sometimes they would need to pay to get rid of it. Ask them if you decide there's any material you would like to have for yourself - fill dirt, blasted waste rock, broken up concrete or asphalt, used culverts (if they don't destroy it when they remove it), trees, etc. I wouldn't bother talking with the state about any of this type of stuff, they won't be able to write up details like this in their plans and specifications package anyhow. Just wait till the contractor shows up on site, and deal directly with him. They have a lot more flexibility once they're on site.
Good luck!
John