In principle, it can be done both ways, just one is more complicated.
- Wiping if there was sensitive data before (eg. with dd on a spinning HDD, or the builtin Erase feature of SSDs)
- Installing the OS and choosing to encrypt the partitions there
- Installing the OS
- Making a full backup to another medium
- Using a LiveCD etc. to wipe the first hard disk
- Create encrypted partitions there
- copy the files back to the new encrypted partitions
- Fix bootloader etc.
- Wipe the second hard disk (the one that was used temporarly for storing the backup)
And it depends on the specific software that is used.
- LUKS on Linux can be used during the installation already (depending on the distribution at least)
- (not sure about Bitlocker on Windows right now)
- Veracrypt (I don't recommend it for such things): neither Windows nor Linux support it out of the box, and of course it's not supported in their installer either. Still, encrypting the OS partition manually later appears to be possible now (at least for cases that are not too complicated), with some third-party tools.
For "method of encryption", the default settings of LUKS etc. are fine (nowadays it's AES-XTS and so on).
And for the benefits on hard disk encryption, there are probably more complete answers out there, but in short: If the laptop is stolen and turned off, nobody can see your secret files. It does not help if the laptop is turned on. And if it was stolen and you get it back, you can't trust it even if it was encrypted.