I would suggest you continue playing your Seasonal Character in Adventure Mode. Even if you don’t get very far, it will let you get familiar with what you can expect when Season 19 starts.
When Season 18 ends and your Seasonal Character is converted to non-Season there will be 1 or 2 weeks before Season 19 begins. During this time you can play your now non-Season Character through Campaign Mode if you’re interested in following the story line. Plus it will allow you to unlock Adventure Mode in non-Season.
When the new Season starts you can stash all your and your Followers’ gear or salvage anything you don’t want to keep. With your Character and Followers completely naked you can Rebirth your Character as a Seasonal Character. You will start all over again with your Character at Level 1 and 0 Paragon Points. But, you will retain Lifetime Kills and Time Played.
Or you can just create a new Seasonal Character.
Note: If you choose to Rebirth your Character and you forget to remove their and their Followers’ gear, those items will be mailed to your non-Season. In this case, you’ll want to create a non-Season Character to collect the items from your non-Season, in-game mail. If the items are not collected within 30 days, the mail gets deleted. If you remember to remove all gear and stash it, you won’t have to worry about checking your non-Season mail.
Also note: If you have a non-Season Character that has completed Campaign Mode through Act V (killed Malthael) and unlocked Adventure Mode, do not delete that Character… ever. Doing so will cause Adventure Mode to lock again. Some players say that rebirthing a Character does the same thing.
You might also want to take a look at this Season Leveling Guide:
Good luck and good hunting! 