Create a new folder under the 'Local Folders' heading at the bottom of the folder pane. Then go to Account Settings > Copies & Folders and set the folder for sent messages accordingly. Bear in mind that some email providers automatically keep a copy of sent messages on the server, so you will probably want to unsubscribe from that folder; you may also need to keep an eye on it and empty it periodically to stay within your usage limit. Bear in mind also that Local Folders aren't backed up to the server, so you'll need to keep regular backup copies of your Thunderbird profile folder in case of machine failure etc.

Read up on the differences between POP and IMAP. Maybe POP would work better for you.

Thanks for the reply, all sorted now.