I've spotted at every large London station and taken thousands of photos - very rarely get even noticed by the station staff. Just stay behind the yellow line, stay out of the way of passengers and you'll be fine.
Clapham Junction usually has a dozen or more spotters.
On the GWR - Hanwell is nice and quiet but all passing HSTs, Heathrow Express and many locals, with good freight traffic. All the stations within the Oyster have low fencing on the fast platforms at present, but you can lean over.
43188 on a Bristol to Paddington service by
Timothy Young, on Flickr
On the Chilterns, South or West Ruislip are nice and quiet but with all the loco hauled services. Rare freight.
DVT 82302 on the tail of 1K50 for Kidderminster by
Timothy Young, on Flickr
You can also spot from the Underground stations along the Jubilee line which runs alongside the Chilterns - West Hampstead is great, but tube trains take up the whole platform and can block your view and you might get asked to move along.
DVT 82304 with a layer of snow on top by
Timothy Young, on Flickr
For the full on freight and passenger experience, Stratford is probably best - all the freight off the North London line, plus a wide variety of units and 90 hauled Anglia trains.
I also enjoy the North London Line - lots of freights, varied stations and safe in daylight
60056 passing Homerton station by
Timothy Young, on Flickr