Just buy a Super Off Peak Day Travelcard on the day of travel from one of the ticket offices or the ticket machine on the day of travel. This costs £19.00 and allows you to make one return journey to London and unlimited underground, national rail and buses is fare zones 1-6 (there are a couple of exceptions but we don’t need to worry about them here).
The LNER only fare is a little cheaper although the service is less frequent, especially on the return.
Then catch the first fast train that arrives, Thameslink have 4 fast trains an hour (xx02,xx17,xx32,xx47) that only call at Finsbury Park. LNER have one or two trains an hour that are non-stop but the time saving is marginal. Don’t get the Thameslink trains at xx10 or xx40 as these are slow.
No need for seat reservations, just turn up and go.