I use smsbackup+, a free app in the play store, to backup all conversations to a label on my gmail account. It's automatic, backing up within a few minutes of receiving a message (so you can delete something unimportant before it backs up) and every hour otherwise (though you can configure that to be more or less often) to back up what you've sent. I like it because I just done have to think about it - it just backs up. Then you should be able to use a standard mail app on your computer to copy conversations to your pc.