OK, that should be good enough. Here we go.
First, it looks like this is your Mac:
http://www.everymac.com/systems/app...-15-early-2011-unibody-thunderbolt-specs.html
Your internal hard drive is certainly not a speed demon, spinning at 5400 rpm. When I purchased my Mac MIni, it had a 1 TB slow 5400 rpm hard drive, but a few months later, I replaced it with a fast Samsung 840 Pro 256 gig SSD, and was my "need for speed" definitely satisfied! Also, that 1 TB drive went inside a nice, slim Orico external enclosure which I have used for backups and storing stuff. It especially came in handy when we traveled, as I could hook it up to my 13" Mid 2013 MacBook Air and watch videos on those long flights.
Secondly, the USB ports on your Mac are USB 2.0, which is OK. Also, the SATA connection for the internal drive is 6.0 Gb/s SATA 3.0. That is about the fastest you can get.
Third, this link shows how to replace your internal hard drive with another one:
https://www.ifixit.com/Guide/MacBook+Pro+15-Inch+Unibody+Early+2011+Hard+Drive+Replacement/5895
Those same instructions are valid for using an SSD instead.
Now, here is that Orico external enclosure I was talking about:
https://www.newegg.com/Product/Prod...ATCH&Description=Orico+2189U3&N=-1&isNodeId=1
You can also get it from Amazon for the same price, but unless you have a Prime account, or order other items together, shipping will not be free.
I have 2 such enclosures, and they are really neat! Small, slim, and light, and my Samsung 850 Pro 512 gig SSDs fit inside perfectly. (Your internal drive, or a new HDD (needs to be a 2.5" model), will also fit inside).
Now, before opening up your Mac (per the instructions above), you'll need to purchase the HDD or SSD, install it inside an Orico external case, and then do the following:
1. Connect it to your Mac (you can use your "good" Mac for this, ie, your 2013 13" MacBook Pro).
2. Use Disk Utility to Erase, Format, and if necessary, Partition that HDD/SSD.
3. Do a clean. "virgin" installation of the Mac OS you want to use. The best way to do that is to first visit the App Store and download the latest version of whatever OS you want. If it's Sierra, that version would be 10.12.3. Just click on "Featured", and on the list to the right, you'll see macOS Sierra. If you want an earlier OS, if you have downloaded it before via the App Store, you should see it in your "Purchased" list. If not, maybe someone else could help you about getting it.
In any event, when you download that file, inside your Applications folder will be a file entitled "Install macOS Sierra". The first thing to do is to make a copy of it in another location on your hard drive (you'll also do this later after the installation onto your new HDD/SSD). The reason is that after you launch it from your Applications folder and the installation completes, that file disappears. Hence, it's a good idea to have another copy someplace else.
Now, to confirm, you stated that there is nothing critical on your current drive on the 2011 MacBook Pro that you need. You'll need to confirm that, as the rest of the instructions are based on that assumption.
Once the installation of the OS is done, for that extra copy of Sierra (you did remember to do that, right?), make a copy of it someplace on your new HDD/SSD.
By the way, when you do that installation, it will also automatically create the new, clean (hidden) Recovery HD partition.
Given that you did a clean, "virgin" installation of the OS, and that you are not getting anything from your current drive, you'll need to go through all the initial setup information for that drive and the OS.
Finally, once you complete that, shut off your Mac, remove the new HDD/SDD from the Orico enclosure, and follow the instructions above about replacing your internal hard drive on your 2011 MacBook Pro with the new HDD/SSD. Make sure you have the tools they state you need. And then install your old HDD inside the Orico case.
Boot up your Mac, connect the Orico enclosure to it, and then use Disk Utility to do whatever you want with the stuff on the old HDD. You could first have Disk Utility perform First Aid on that drive, and that should tell you how healthy the drive is. If it's still OK, then you can use Disk Utility to Erase and Format (and if necessary, Partition) the drive, and start to put stuff on it. In fact, you might want to consider using that drive for back up purposes.
The final thing is you need to decide the following:
1. Purchase a new HDD, or a new SSD.
2. How "big", in terms of gigabytes, a device you need.
3. What is your budget?
As for how "big", as I mentioned, that's going to depend on how much stuff you want to store on the internal drive. As it is, the installation of Sierra is going to take up some space, but not too much. However, as long as your old hard drive is healthy, you could store stuff on it (if you are going to use that drive for backup purposes, you will need to first partition it (I mentioned that above), with one of the partitions being for your backup. Once again, the amount of space you'll need for that is up to you. However, if you use Time Machine to make backups, you might need a larger capacity drive. There are a couple of other backup programs available that are excellent, and in fact the backup will take up MUCH less space).
I of course do not know where you are located, but here in the US, with Presidents' day coming soon, there will most likely be some good sales on a variety of stuff, including HDDs/SSDs. If you can provide more detailed information about whether you want to purchase a HDD or SSD, I (and probably others) can help you with that.
