Train fares from Liverpool Street
Stansted £21 single
Southend £14.30 single
(I used Prittlewell as illustration for Southend fare, as the price to the airport station hasn't been loaded into the railway ticket pricing system yet).
As to early morning service. It isn't beyond the bounds of possibility for the train operator* to adjust the schedule. I'm sure there used to be an earlier train (first job was in Essex, remember having to do stupdily early start some days).
* Now that Dept for Transport micro manage the railways, maybe it is impossible for the train operator to adjust the schedule....