The driller should have done a pumping test to determine flow rate versus drawdown. You should also have a water test that tells you hardness, pH, coliform (shouldn't be any), iron, and a few other chemicals. You should also get information on turbidity and suspended solids, which will tell you if you may need a filter.
You negotiate best when you have knowledge. Here is some information that might be useful to you.
Assuming a combination of well drawdown and pressure drop in the pipe totalling 80 ft, A Goulds 10GS07 pump (10 GPM 3/4 HP) will give you 11.5 GPM at 60 psi and 15.8 GPM at 20 psi. The next size pump (13GS10, 13 GPM 1 HP) would give you 14.1 and 19.4 GPM at the same pressure conditions and might risk overpumping your well.
You should ask if you are getting a 2-wire or 3-wire motor with the basic system. The 3-wire pump requires a control box but the motor is less expensive so there is little difference in the pump/control cost. An additional wire to the pump is required (3 conductors + ground wire). It is also necessary if you are ever going to add the constant pressure feature.
You shouldn't care if he uses wire in PVC conduit or code-compliant Underground Feeder Wire buried in the same trench that contains the pipe. Both of them are required to be below the depth where anyone should be digging and PVC conduit doesn't provide much more protection. It probably costs about the same.
If you think you would ever upgrade to constant pressure, or if you think you might ever up-size the pump, then you should get 3-wire and wire size to handle any upgrade. Find out what wire size you are getting and make sure it will do what you may want to do in the future.
There was a long discussion on check valves a few weeks ago and there are differences of opinion on whether an extra check valve (it really isn't a foot valve) is required or appropriate. There is a check valve in the Goulds pump. Check valves cost about $20 but it requires two extra fittings and some risk of failure down the well. However, it is also a backup if the check valve in the pump fails.
Increasing the warranty to 5 years on parts-only doesn't mean much to you. Nothing should fail in 5 years and his charge for labor will be the biggest part of any repair project.
The upgrades for tanks from 20 to 40 and from 20 to 80 are $86 and $165 in my Grainger catalog. Your supplier will have a markup but should be able to do better. The 20 gallon tank is probably too small for a pump that will be operating at around 13 GPM. The available drawdown for a 30 to 50 psi pressure range is only 5.9 gallons, so the pump cycles will often be less than 30 seconds. Your supplier knows it's too small so he is offering you an upgrade.
I would ask what he would use for hardware other than brass and stainless in the basic system. Aside from the black plastic pipe coming in from the pump, I would expect brass fittings. There shouldn't be any galvanized or plastic or black iron in such an installation.
The constant pressure system requires a controller that substitutes for the control box in a 3-wire system. The difference in price to your supplier for adding constant pressure to a 3-wire system will be about $400 to $450. If you get the constant pressure system you would not need a tank upgrade but I would still not go smaller than the 20 gallon tank.
There are probably more things but I can't think of them now.