Actually the first line did not go to Temple Meads but was built from Hotwells to Avonmouth and called the Bristol Port Railway and Pier (BPR). Work began on the line in 1863 and was opened two years later on 6th March 1865 with six trains each way on weekdays and four on Sundays. The stations were Clifton (between where Bridge Valley Road is now and the Suspension Bridge), Sea Mills, Shirehampton and Avonmouth. The station at Avonmouth was not in the same place as the current one, but there have been so many different stations in the Avonmouth area that it's pretty difficult to work out which station was where.
There were various plans to extend the railway into the centre of Bristol and to Temple Meads but they came to nothing, partly because of the precarious state of the BPR's finances. This meant, of course, that the railway was totally isolated from the rest of the network.
Meanwhile the Great Western Railway and theMidland Railwaydecided to build a joint line and on October 1st 1874 the Clifton Extension Railway was opened from Temple Meads to Clifton Down with intermediate stations at Lawrence Hill, Stapleton Road and Montpellier. It had been hoped to have passenger traffic all the way through to Avonmouth, but the tunnel under The Downs was not finished and there were problems with the length of the platforms at Sea Mills. The section from Clifton DOwn to Sneyd Park Junction (where the new railway met the BPR) was first opened eleven years later on Sept 1st 1885.
Now, of course, there were two stations with the name Clifton, so in 1891 the end station of the BPR was changed to Hotwells. The station survived until July 1922 when it (and the track up to Sneyd Park Junction) was removed in order to make way for the building of a new road from Avonmouth to Bristol: The Portway.
The residents of Redland petitioned for a station there and in April 1897 one was opened close to the Lovers Walk railway bridge and with the ticket office actually on the bridge and not down on the platform. St. Andrews Road was opened in March 1917 in order to serve the munitions factory there which was expected to help with the war effort. Finally Severn Beach station was opened in April 1922 and quickly became a popular destination. For example it is said that the Whit Monday of 1922 saw packed trains arriving at Severn Beach all morning and half the afternoon, and remember, then the trains consisted of a locomotive plus five or six coaches!