Don't worry, I'm not the person who says storm razor or blade of the ruined king.
The far more intellectual answer is building thornmail
first.
[slayer-jinx-wink]
But new player, don't actually build this first. This is a joke.
On a serious note, does the new player already know how to find items by searching the name? Or the full items you listed are all on the recommended page? Does the player know the items?
Also, is the new player playing the twisted treeline game mode? Maybe that is why you get gold a bit slower? Not sure if you want to play Summoner Rift against bots.
Doran's items are gold efficient items that helps you last in lane in the early game(when you farm minions in the first 10-15 minutes of the games on the Summoner Rift map) but you can't use them to build them into anything.
How much gold you get depends on your minion count (next to your game timer on the top right) and your kills. The higher the minion count you can get it to, the more gold you get.(Hopefully, you won't get some weird ideas from reading this.)