I have a slow - class 4 4GB card which came with the camera and a 32GB 45mbps which I bought. I use the 32GB mostly, but rarely accumulate more than 500 images. The card can hold an estimated 1600 RAW files. If I had to buy today, I would go for either the 8GB or the 16GB, which ever gives better deal.
The only reason I got the 32GB card was the cost - it was quite close to the 16GB price. The problem with a large number of files on a card is the time it takes for the directory listing to appear on the computer. I only use USB cable for data transfer. If the D3300 had a USB3 port, then the transfer would be much faster.
One should never keep the images on the card for storage purpose.
. It is more expensive than an external dis - 1TB USB3 disk is less than a hundred US dollars, at least five times less than the cheapest card.
. You have to transfer the images to a computer any way, whether to process them further or to archive them.
. Transferring the data to an external disk gives you a backup copy.
. In case the card gets corrupted, all your images are lost.
The only reason to use a large storage space in form of cards, is when you are away from your computer, say on a long trip and cannot transfer the images. In that case multiple cards are a better option, along with some method of keeping copies (in case there is only one slot)