Last bit first:
Connecting two Windows computers together isn't as simple as connecting them with a USB lead. You need to establish a network between them. (The simplest way is to create a network via your router, rather than using any type of lead between the computers). However you shouldn't need to do that anyway as you can simply plug your USB memory stick into your new laptop, and then access your photos directly, without any problems.
If you can afford the price, your best option for storing and viewing photos might be an iPad. That's because:
(a) they've got exceptionally good quality screens (so your photos will look their best) ; and
(b) they've got a 4:3 screen aspect ratio (which matches the ratio used by most digital cameras, so your photos can fill the screen). Android tablets usually have a 16:9 aspect ratio ;
(c) they've got a longer battery life than many Android tablets.
However, at a far cheaper price, an Amazon Fire (for just £49.99) would still meet your needs quite well, even though you'd need to install a microSD card if you've got lots of photos to be stored. (You can buy a 32Gb card online for around a fiver. It will hold over 15,000 photos taken on a 6Mp camera. Should you need it, you can use a card up to 128Gb in the Amazon Fire).
See the reviews here:
http://www.pcadvisor.co.uk/test-centre/tablets/best-tablet-best-tablets-best-tablet-2016-20-best-tablets-2016-uk-3265725/