Ok, OST is only with Exchange or iMap, it is the way to go but only if your email service provide has this functionality, then when you make folders it make them on the server and it is shared across multiple computers, this is the only way to achieve this, it is via iMap.
What you do is if you can connect using iMap, then you add the account on the old computer via iMap, then drag the folders to it, it will then upload the folders to the server.
Then when the second computer connects, you connect it also via iMap and it will download the folders as well, not just the inbox which is what you get with Pop3 (that you currently have)
Another way is to add the accounts on the new computer as iMap accounts, then copy over the PST files to the new computer.
Then go to File, Import and import the PST files into the account. Either way will accomplish this.