Hi gracie22,
Thanks for your interest in using the classifieds to sell.
It's recommended putting sold on an item for at least a few days before deleting. Reason being someone very possibly was browsing the item previously, coming back to check it out and spending potentially a lot of time trying to find it. If it's listed on the site but marked as sold then they will have their answer quickly rather than being left wondering. I actually get the odd tech support request from people that have spent a lot of time searching for a deleted ad... the more of those situations we can prevent the better.
Of course it's completely respected that some will have their own personal reasons for deleting right away, which is why the delete button is always there as an option any time.
Also, regarding browsing ads that aren't sold you might want to consider checking out the drop down menu that's on each ad listing/category listing page on the website that allows you to choose to only see ads that aren't sold.
Cheers