Hi,
As its on the Arena circuit best to follow the new signs to find were you are going, but the best places would be..
If you want to shoot through heavy fencing the places would be..
Copse outside (will need more than 300mm but cropping should be fine)
Maggots (panning through fencing

)
Becketts inside (get the cars head on, just before they head down the wellington straight)
Aintree and the loop, ( there is a grandstand or 3 at the new arena section, but below you can shoot the rear of the cars, especially if they will flame
Farm corner (if they allow public into the area) Head on shots looking down to club corner
Places to shoot without fencing would be (need a 300-600mm to shoot there without media accred to get decent shots)
Stowe (In the grandstand looking down the hanger straight you can get a decent pack shot on the first few laps)
Vale (up on banking you can shoot down and pan the cars as they come around vale, also there is a new gravel trap which does catch people out...
Abbey (as the cars come into the abbey curve you will have to be quick to pan them just before they turn in)
Finally Luffield (the most commen place were non accredited togs photograph, as you can see over the fence when stood high enough to get head on and good pack shots, also you can see the whole of brooklands.
I hope I could help with places to shoot??
Shutter speeds would have to be around 1/320th - 1/500th for head on shots.
If you are panning try to get as much wheel movement as possible, so start around 1/200th & work your way down and down, until you reach a shutter speed where you find it hard to get the cars fully focused and sharp..