'One' services from Southend Victoria (into Liverpool Street) and c2c services from Southend Central (into Fenchurch Street) both take roughly between 55 and 75 minutes. The off-peak day return fare is �12.50 from Central or �12.30 from Victoria. Both stations will give you the option of adding a one day Travelcard onto the same ticket for about a fiver extra. Alternatively, you can buy an off-peak one day Travelcard (for Zones 1 & 2, which covers most of the tourist areas) for �5.30 when you arrive in London.
As has been stated, Oystercards are only valid from Upminster when using the line into Fenchurch Street. If you use the line into Liverpool Street, Oystercards aren't valid until Stratford. If you get an Oystercard and only use it for off-peak travel in Zones 1 and 2, you'll be charged �4.80 per day. (Although it might seem tempting to travel from Southend to Upminster or Stratford on a National Rail ticket and then switch to using an Oystercard that's probably not advisable because you'd have to alight from one train, exit the ticket barrier and then re-enter before boarding another train; Oystercard only works properly if you use it at the start and end of each journey for which its valid).
The previous paragraph assumes that you load your Oystercard with cash. You can also (somewhat confusingly) load it with a one week Travelcard (which can't be purchased as a normal ticket). For use in Zones 1 & 2 only, that will cost you �24.20 (plus the �3 deposit on the Oystercard).
http://www.tfl.gov.uk/assets/downloads/guide-t o-fares-and-tickets-08-01-02.pdf
Chris