If you shut down your PC and then restart, the Bitcoin sync will pick up where it left off.
The latest transaction your Bitcoin currently knows about is 7 years old, but it won't take 7 years to catch up. It should be all caught up in a matter of days.
You will need a lot of storage for Bitcoin Qt. The current size of the blockchain is over 80 GB, and grows at about 4 GB per month. The blockchain is always growing so you will continue to need more space indefinitely.
If you want to use Bitcoin but don't want to store the entire blockchain forever, consider using an SPV client. See the question What is an SPV client? for more information.