I'd like to think I know a fair bit about hardware so bare with me.
problems with option 1 - laptop's perfectly fine, the 710M seems a bit redundant really considering its almost useless when it comes to games - it is that bad. if you like you should find a cheaper alternative with integrated graphics.
then there's the PS4 - i'd look at what games are actually available, and how many you would actually want to play. I know for me that the main game I want to play isn't on PS4 so i don't want it.
option 2. £800 - if you look at a custom build you can get one that's far more appropriate for gaming, the only trouble is that the battery life then sucks on them, regardless of what they try to advertise.
HOWEVER
there's a way around the crappy battery life in the form of portable USB laptop chargers - it's basically a USB power brick that depending on the one you get will keep your laptop going for another few hours. Link here for more information:
http://www.techradar.com/news/portable-devices/other-devices/best-portable-chargers-14-we-recommend-1178873The best custom configuration for £800 is found here:
http://www.pcspecialist.co.uk/notebooks/optimusV-13/it's even a 13.3" so it fits nicely in a bag and uses a 765M. However if you wait until the 8th of April, new graphics cards are available that are far better than the ones available now. £764
http://www.pcspecialist.co.uk/notebooks/cosmosII/this is a 15.6" laptop that has a new graphics card (850M) from the new series that have been recently released. it is technically better than the GTX 765M - should end up around £742
If you want help on how to best configure the laptop for the best spec then PM or reply to this post
Option 3
the GTX 650 is a terrible card, its actually worse than the gtx 765M, although the low-mid laptop may have decent battery life?
hope this helps on your perspective.