I'm local to Finsbury Park and when I needed to get to Slough cheaply I would get the Piccadilly Line to Hounslow West then the 81. If you value your sanity I can't recommend it on a daily basis - it is about two hours each way vs about 70-90 minutes via Paddington and a fast train. It is the cheapest practical way of doing it, though (£55.20/week vs £82.10).
The more learned members of this community will be along to suggest travelcard splits and the like if such an option exists.
An Anytime Day Return from Finsbury Park to Slough is £15.60 for travel by National Rail to Kings X or Moorgate, then Underground to Paddington, then National Rail to Slough. Five of these will be less than a weekly travelcard, and twenty of these will cost the same as a monthly travelcard. (If you have a 16-25 railcard, the price will be nearer £10.25 per day during July & August, and £12 per day for the rest of the year.)
A Slough to Zones 1-6 travelcard is £82.10 for a week, £315.30 for a month and £3,284 for a year (and a Slough to Zones 2 to 6 weekly travelcard is £61.60 if you can find a route that avoids Zone 1 but which is likely to be considerably slower). These will be the travelcards you need even though you start from Finsbury Park rather than Slough.
A travelcard is cheaper for travelling five days per week than a Slough-Paddington season ticket and then using Oyster/contactless to travel Paddington-Finsbury Park by underground.