Travelcard or Contactless?

First you need to clarify, is this a simply round trip from Petersfield to a zone 1 Underground station or will you be travelling around central London before returning?

According to the NR and TfL websites, and assuming no railcards.

Off peak: valid on and from 0857
Petersfield - Waterloo off peak day return with travelcard add on £38.20:

Petersfield - Waterloo retrun off peak day return £31.60
Waterloo - Baker Street £2.20 each way
Total £36

Petersfield to Wembley Stadium off peak day return (via Waterloo and Baker Street/Marylebone)
£34.70 between 9am and 3pm, or
£29 if outward journey starts after 1500.
Break of journey is allowed, and obviously you don't actually need to go to Wembley and back!

Peak rate (before 9am)
Petersfield - Waterloo return with travelcard add on £58.10

Petersfiled Waterloo return £50.90 peak rate
Tube £2.20 each way
Total £55.30

Petersfield to Wembley Stadium peak rate return - £57.10

So the travelcard add on is not worth it for a simple there and back, and at off peak times getting a cross-London ticket (which includes tube travel between NR termini - and Baker Street counts for these purposes) can be even cheaper. (Finsbury Park or Bethnal Green are 40p cheaper still, but may lead to awkward questions if you are going to Baker Street!)