I've conducted a certain amount of research into the mass scanning of photos without spending hours at a scanner and come to the conclusion that broadly speaking there isn't an especially good home solution.
There are various companies who will do bulk scanning for you, either in your own country or slightly cheaper if they ship the photos somewhere like India. All of them seem to work on a similar basis - relatively cheap for a basic scan, but more for restoration of colour, or removal from albums. They seem to use some quite costly high quality scanners. ScanCafe would be an example of such a service. They'll usually either send the photos back to you on DVDs/USBs, or make them available as downloads. Look to pay 20c an image. Of course you're putting your trust heavily in couriers/delivery companies which is the scariest thing about this. But they handle it all for you.
For home scanning there's nothing really there. I actually own a document scanner - the Fujitsu iX500. This handles paper really well and is great for documents you want scanned. It scans the documents as fast as the massive copiers in an office/copy-centre might scan them. But it's really not suitable for quality photos. It'll do them, but not great.
Sadly, I think it's a laborious home process if you're not going to "outsource" the problem. I guess if you've got kids you might be able to incetivise them to do it well for something. Or maybe it's a dull task you can do while watching your favourite not-terribly-demanding boxset.
As to where you save the photos, I can offer a few thoughts.
Flickr: Free for the first 1TB of photos. This is a massive amount - and should account for tens of thousands of photos. Obviously it's owned by Yahoo which is in the process of being sold to Verizon. I've been a "Pro" user for more than ten years now, which removes ads. I have over 17,000 photos and that uses less than 100GB, so loads of room. Flickr hasn't been developed as much as it should have been, but it does allow me to easily embed photos elsewhere, and you can change the privacy settings as you wish, including letting friends and family have access to albums even if they're not Flickr members themselves. (There's also an app that can upload copies of all your mobile photos direct to Flickr)
Google Photos (was Picasa): Basically you get this free with a Google/Gmail account. They allow unlimited uploads if you keep the resolution below 16 megapixels. Depending on how you scan your photos, you'll probably find that you can get in under this limit and essentially get free storage from Google. If your photos are massive, then you start to use the space in Google Drive (starts at 25GB I believe). You can choose whether photos are private or public. (You can also get an app to upload copies of all your mobile photos direct to Google Photos).
Imagur: Don't know anything about this.
Amazon: Also has a photos backup service for Prime members. Amazon's plan allows unlimited photo uploads regardless of size. Great if you've already got Prime.
One way or another, if you're digitising your photos, I thoroughly recommend finding somewhere online to save your photos even if they're not for public display. I've recently been embarking on a big backup plan for all my data so it's safely stored both at home and online somewhere. I'm actually paying for Amazon Drive which in the UK is an extra premium on top of my Amazon Prime account. But since it's unlimited it means I can store nearly anything - photos, home video, music etc. (I think most of these service are a bit "funny" about storing video files you might have acquired elsewhere).
Sadly I think in a digital world, far too many of us don't think about storage properly. I still remember an old work colleague who had a burglary at home and lost an external hard drive that had all his photos on it. They weren't backed up anywhere else and despite the drive being low value, he lost priceless images.
Adam