I think that you are in zone 4, so you will need a pass for zones 4,3,2,1 - zone 1 is central. The day pass is £3.60, a weekly pass is about £23.
Try looking at http://www.users.dircon.co.uk/~zzyzx/tourist/tube.htm#zone
Also, a search for "London Underground" will give you all the info that you need.

Just to let you know that Finsbury Park is in zone 2, so you will only need a travelpass for zones 1 and 2.

I purchased a London Visitor travel pass for about $20 US from a travel agent in the States. This pass was good for 5 days on all buses, tube, and surface trains within 15 miles of central London. Zones were of no consequence. You should definitely get the visitor travel pass rather than a tube pass. The surface trains are much better for travel outside the city center. The tube can be surprisingly slow over longer distances although essential for sprints within the city (surface streets are jammed). Surface trains can be designated as slow (local with stops), semi-fast (stops at major centers), and fast (express to suburban cities). Buses are plentiful but irrational in schedule and route (mostly because of the impossibly confusing road system). However, I used the buses quite a bit and the travel pass is a must; the fare structure is worse than the route structure! Don't forget cabs. London cabs are generally cheaper than many other big cities (cheap being a relative term) and the cabbies are all the equivilent of PhD Geographers. Travel in London is a bewildering but delightful adventure. London itself is a world class gem of urban tourism. Enjoy!

Whoops! seems as if got the zone wrong for Finsbury Park, no matter, there is always someone to correct our mistakes. However, I do not think that London cabs are cheap. I did get the web site right, didn't I?