I use any reasonably priced 2.5" SATA SSD installed into a suitably sized USB caddy. I have 9 of these of varying sizes all performing various jobs. Back-ups are one of them as well using some for booting into different versions of the macOS. Been doing this for years. I source the cheapest I can find on the internet, usually Amazon and eBay. All of them work well and have never failed unlike the IDE and SATA drives I used prior to moving to SSDs.
In my experience any size Sandisk and Samsung branded SSDs work fine as do Crucial and Western Digital. Bear in mind the first back-up, regardless of what you use software or hardware, is always going to take time. The more there is the longer it takes. 950GB of data is a lot and if you're backing all of that to a 1TB drive then you're not allowing for the "10% rule". I'm not surprised its taking even longer and probably the last 100GB or so is taking the longest time of all.
In a nutshell the 10% rule is you must leave at least 10% of free space left on whatever capacity drive you're using. So for a 1TB drive it's a 100GB and so on. Think of it a little like filling a pail of water. If you fill it right to the brim you'll spill some and make it more awkward to carry. But if you fill it to a reasonable level it becomes easier to carry and you won't spill a drop.