There are three direct choices for London to Birmingham.
In order of speed they are:-
Virgin Train West Coast from London Euston to Birmingham International and Birmingham New Street with some continuing on to stop at Sandwell and Dudley on their way to Wolverhampton. New Street and International have 3 trains an hour most hours. Travels at up to 125 mph. Also most expensive.
London Midland from London Euston one stop (Milton Keynes Central) on the way to Rugby where you change to a London Midland train to Coventry, intermediate stations including International and terminates at Birmingham New Street. Travels at up to 110 mph. Cheapest.
London Midland also run trains with no change required which take somewhat longer because they stop more frequently and have a longer stop at Northampton, traveling at similar speeds. Same price as the faster London Midland service.
Chiltern Railways from London Marylebone via Banbury to Birmingham Moor Street and Birmingham Snow Hill, with some intermediate stops. It travels somewhat slower and is not electrified. The price is less than Virgin.
It would be helpful if you could share what part of Birmingham you are needing.