I understand that it is a little late for the original poster but for anyone else who is thinking of coming to Chesterfield then here is basic info from a local.
The bridge to the north of the station is about 5 - 10 minute work from the station. If you have a car then you can park at the bottom of the bridge and there is space for at least 2 - 3 cars, I've parked there hundreds of times. There are no 'facilities' of any kind so come prepared weather / food wise. For photos the only problem you might have is the sun (as the line runs north / south) and a very annoying phone wire that occasionally get's in shots. Have a look at my flickr and you will see hundreds of shots from the bridge and I have a link to this year's photos:-
https://www.flickr.com/photos/66737297@N06/albums/72157663482217545
The station itself is very spotter friendly but there is no 'free' parking as such. You might get away with it for a little bit but I would not try for too long.
The staff are all very friendly and I have never had any issues at all here. There are no barriers, a newsagent (run by the same bloke who has been their since I was a boy and I'm 47!), a café and ticket office / waiting rooms.
The station has 3 platforms but number 3 is not often used unless their is any disruption when it can be used to allow trains to over take on the mainline.
Platform 1 & 2 see 90% of passenger traffic (XC, EMT, NR) and a fair bit of stone / aggregate / cement traffic up to the Peak quarries. 'Round the back' run two freight lines which can all be photographed from platform 3. An example is here:-
https://www.flickr.com/photos/66737297@N06/24231826172/in/album-72157663482217545/
Freight tends to come in bursts. We have upwards of 40 freight trains a day but a lot runs at night. Always check RTT to make sure you do not hit a quiet period.
We also have a large number of light engine moves between Toton / Peak Forest /Doncaster and Network Rail test trains often run through from / to Derby. Finally, if you are in the area on a weekend Barrow Hill Roundhouse is open (and free) most weekends.
If you do get the chance to get into town then it is only a few minutes walk uphill from the station. Head towards the Crooked Spire (you cannot miss it) and you will find everything you need.
Andy S