Need a new internal 1T SSD (not hybrid)

Faster SSD drives are NVMe drives and need the correct hardware architecture inside. I have a 2016 Lenovo computer with PCI-e NVMe SSD capability and I have a 1 TB Samsung 960 in the machine. It is indeed speedy.

You need to make sure the older MAC book can take the faster drive. I am not sure it can.

I did some looking and it appears it is possible to use an NVMe drive in your MAC book.

https://apple.stackexchange.com/questions/287644/do-macbooks-support-nvme-ssd-drives-via-the-use-of-a-sintech-adapter

SSDs nowdays are quite reliable so i guess it wouldn't matter which brand you choose ...just pick one of the big boys (Crucial,Samsung,Kingston,Intel,Corsair,Adata ...the list goes on..) ...but do remember that nothing is 100% ....so pick your drive...carefully replace your old one BUT keep the old one ....it would be better to keep it intact as its working now....of course just delete whatever is not crucial to make room...probably buy a case to turn it to external one and use it as backup...whatever is important just try to keep them in sync (new <-->old) ..so if something goes wrong...just popup the lid (sorry i am not aware of Mac's disassembly procedure ...a lot of money ..i just don't have) ...take out the "new"...put back the "old"...you are back working..

Oh, and if your MacBookPro has an optical (DVD) Drive and you don’t use it, you can get an “internal mounting bracket” to put the old drive where the DVD Drive was, removing the DVD Drive, and then have both your new SSD Drive and your old drive available. I did this and moved all my pictures to the HD as I did not need speedy access to them.

Apple stopped DVD drives around 2013, so not sure if yours has it or not. Just throwing out an option, and OWC sells those too.

John, you were not far off. You pop off the bottom and the drive is immedialty visible in one corner.

Note to author: When you remove the bottom, be sure you have the right tools. (OWC will often send a small set of needed tools if you ask). Put some double sides sticky tape on your work surface to hold the screws, and put then in a pattern so you put them back in the same place they came out. Many of them are different sizes.

 When you open the bottom you wiill see the drive in the corner. There are two small  brackets hold it in place. Once removed, the drive removes easily. Don’t forget tp remove the small little screw stubs from the side of the old drive and put them on the new drive. They hold the drive in place.

There are a number of videos on YouTube to watch and see it done, and I recommend watching some to be sure you see how it is done before starting. It is easy, but errors can be made.

it looks like your system can take the drive - but will you benefit from a greater speed?  not sure; look here :  https://www.velocitymicro.com/blog/nvme-vs-m-2-vs-sata-whats-the-difference/

It needs a high speed connection/bus to work at top speed. All you can do is try and see how it at.

I think I will follow all this advice and:

1- remove my DVD drive
2 - insert an SSD drive
3 - make it a lower cost 500 GB drive

this gives me 1T combined.

I did not relish this kind of solution since Time Machine backups would become a pain in the neck, true? I suspect I would need external drives which need to e marked as "C:" and "D:" for example.

Given this new hardware configuration, what technology would be best for the 500GB SSD?

i just bought kingston 480 GB SSD's for 70 Euro

I also have a 2013 Macbook and out a 1TB SSD drive in last year, no regrets at all.
And ditto the above comment about macsales.com. Their support is almost as good as Applecare.

So it does look like this machine may not use the standard 2.5" form factor drive, which means using the old drive may not be an option. OWC can tell you that. (Not sure which model you have)

I still suggest going to Other World Computing  and look at their SSD offerings, and they have Videos on their site on how to replace the drive as well.

(https://eshop.macsales.com/shop/ssd/owc)

Click on MacBookPro button, then find your machine in the list, that will take you to a page of available options.
Find one that you like, and then feel free to check the price of that model on the internet for a better price if you like.
Note that the differences in drive replacements will be speed and size, and both effect price.  

I just think this company will make the update as easy as possible, so I like to support them. And as John Tsioumpris said above, most drives these days work just fine.

Since it's a 2013 Macbook Pro, you can also add flush mount SD Cards and USB memory sticks for storage.

https://www.amazon.com/dp/B00WGARJIS/ref=twister_B00KGVMBDW?_encoding=UTF8&psc=1
https://www.amazon.com/SanDisk-Ultra-128GB-Flash-Drive/dp/B01BGTG2A0/ref=sr_1_8?ie=UTF8&qid=1540414838&sr=8-8&keywords=usb+memory+stick

PS.  OWC is the better place to get Mac replacement/upgrade drives.  You'll be more certain that you'll get the correct version.

thanks