First Surfboard: Funboard or Longboard

Hi everyone, I need advice on buying my first surfboard. I'm 5'2" female and weigh between 100-110lbs.
I've done around 7 lessons in the past 3 months mostly on 9' foam boards. Last week I was able to surf everyday for 7 days. I started again with a 9' foam board. I found it easy so I tried out an 8'6 NSP the next day, then a 7'6 NSP for the remaining 5 days. I also gave a 5'10 fish a try for 30 minutes and was able to catch waves and stand up but unable to maintain my balance.
As for the wave conditions, I'm not very good at describing it, but most of the people around have 1 shortboard and 1 longboard. Most people are walking the nose on the longboards and once the waves get bigger they bring out their shortboards.
I'd like to be able to progress onto a shortboard one day, not necessarily any time soon. Probably like everyone else would like to own a shortboard and a longboard. But for now I can't decide if I should first buy a funboard so I can slowly progress to a shortboard or if I should buy a longboard and stick to renting funboards.
Thanks in advance!
I've done around 7 lessons in the past 3 months mostly on 9' foam boards. Last week I was able to surf everyday for 7 days. I started again with a 9' foam board. I found it easy so I tried out an 8'6 NSP the next day, then a 7'6 NSP for the remaining 5 days. I also gave a 5'10 fish a try for 30 minutes and was able to catch waves and stand up but unable to maintain my balance.
As for the wave conditions, I'm not very good at describing it, but most of the people around have 1 shortboard and 1 longboard. Most people are walking the nose on the longboards and once the waves get bigger they bring out their shortboards.
I'd like to be able to progress onto a shortboard one day, not necessarily any time soon. Probably like everyone else would like to own a shortboard and a longboard. But for now I can't decide if I should first buy a funboard so I can slowly progress to a shortboard or if I should buy a longboard and stick to renting funboards.
Thanks in advance!