As regards a storage solution for all your stuff I cannot imagine an online backup will suffice. Most consumer data packages from your ISP will not have much better than 10 Mb/s up bandwidth. That is 1.25 MB/s. If you want to move 4TB of data it seems to me it'll take you over 37 days to move it. Not good.
You will be much better off with a NAS solution. I use a Synology Diskstation 1515+
at work. Combine that with Western Digital Red 4TB drives
(biggest this NAS will take) and you'll net about 15TB of storage (you "lose"* one drive to RAID-5 and 1TB to the file allocation table). I forget the final cost but all told it was around $1500 (including the drives which are bought separately from the NAS).
I know there was worry about hard drive longevity but the WD-Red drives are built with NAS in mind so while not the speediest performers they are built to last. Additionally, since you have these in a RAID setup, when a drive dies you are ok. Pop out the dead drive and pop in a new one (if two drives go at once you are screwed but that is unlikely). Buy a sixth drive to sit on a shelf and be ready to go in case you worry about shipping time for a new drive.
These NAS stations come with all sorts of extra bells and whistles. For instance it can be your own "cloud" storage device which you can access from anywhere including your cell phones. Upload and download stuff to it just as you would with any other cloud storage service (the ability to do this will depend on your ISP...some don't give you the necessary control over your network to make it happen and setting it up is not easy if you are a new to this) . They can also be added on to down the road if you need even more storage.
You can of course opt for even bigger NAS or more robust fault tolerance. It is all a matter of cost and your pain threshold (how bad it would be to lose the stuff). It also is a single point of failure. If you are robbed or have a fire or a pissed off person goes at it with a bat you are SOL. All of these things can be protected against to some extent but again more money and effort. All things you need to balance when making a decision. Few things will be bullet proof and those that are will cost accordingly.
FTR: I do not work for or own stock in any of these companies. The Synology Diskstation has plenty of competition and it is worth your time to compare other manufacturers. I only mention that one because I have personal experience with it. YMMV.
* I am fully aware of how data striping works and that you do not literally "lose" a drive to it. Just noting you lose that much storage space out of the system to cover the overhead for the RAID. The more drives you have the less "expensive" the RAID becomes (three drives lose 33%, four drives lose 25%, five drives lose 20% and so on).