should i buy the bp at the start of the season or when i finish it F2P?
you should buy it at the start because you can complete 4 tasks a day normally, but with elite BP you can complete 9 tasks a day.
If you are confident that you will finish the BP then there is no reason to wait as you can do more tasks each days this way which means you can claim more repeate rewards aswell.
If you are on the fence whether or not you will have time or motivation to keep playing for the rest of the month then I would advise you to wait and do some levels first and buy it at a level that you deem it good enough for the money spent or you are confident that you will finish the last weeks aswell.