@Cu Chulainn It's nice of them to hide that small detail on page 125 of the
Player's Handbook, rather than putting it with the rest of the information. Thanks for pointing it out.
It's normally better to go with the standard items rather than rolling for starting wealth, since using the example above (Rogue Entertainer) you can get between 91 and 162gps' worth of items of your choice from the limited selection, rather than making a roll and getting a random amount of gps between 40 and 160 and having a larger selection to choose from.
There's certain tricks you can pull as well, at the DM's discretion. Such as the Rogue choosing to take a shortbow and a rapier from the standard items (both costing 25gp each) and then selling both of them at half their standard value (
Player's Handbook, page 144 - Selling Treasures) and then buying two shortswords (10gp each.) This means you end up with an extra 5gp overall at the start of the campaign.
Similarly, an Entertainer can choose a Lute as their starting musical instrument (35gp each) and then sell it and buy a Flute (2gp each) instead, gaining them an additional 15gp.