Farnborough (Main) is outside of the contactless payment area so tickets required.

To answer the first part of your question. Contactless is not valid to Farnborough- you do need a rail ticket.

How many days are you travelling? Six? Five? Four? Less?

A 7 day season is £122.10 while an Anytime Day Return is £23. You'd need to make 6 days of return journeys to save any money with a 7 day season.

Anytime and Offpeak tickets can be bought in advance or or on the day for the same price and do not sell out. They are not restricted to a specific train and can be refunded if not used.

You should not have any problems using a non-UK credit/debit card for payment (there were problem on GWR) but you can buy the tickets from any train operating company for the same price. Do not use Trainline or any other website that charges a booking charges

As per Wex Cel, you are basically going against the flow, so the ticket is quite affordably priced (it would be £41 to go in the opposite direction at the same time).

You can just buy tickets on the day.

To get to Waterloo (for Farnborough) from Central London by Underground is £2.70 or £2.80 each way. So £5.60 day typically.

As you are probably only staying five days it's unlikely to be worth getting a travelcard.

There are no inflexible “ADVANCE” tickets from Waterloo to Farnborough. It’s too short a journey. That avoids confusion. You can buy return tickets or a 7-day season ticket either in advance or on the day. For a season ticket, if you haven’t had one before, you need to go to a National Rail station booking office with a passport-style photograph so the agent can issue a photo card.

Day returns are either “anytime” or “off-peak”. “Off-peak” tickets are valid Monday-Friday on the 09.09 departure from Waterloo to Farnborough and all subsequent departures; and they’re valid all day on Saturdays and Sundays. But, at £22.10, they’re only 90p cheaper than “Anytime” (which seems to me to be verging on the pointless).