If I bought an internal SSD to replace current hard drive for my 2011 MacBook Pro would it take full advantage of a newer SSD say like a 1 TB drive?
There are many tutorials of good quality and reliability which address the issue of drive replacement for a version 8.1 second-generation 2011 MacBook Pro. Many users have found this to be a worthwhile upgrade.
May I suggest you look at the guides on YouTube, starting with those from iFixIt? Those were very popular with the Mac team of the community computer rebuilding/reuse center I volunteered at for many years.
Every PC, MacBook, and MacBook Pro which was donated to us had its HDD or SSD replaced, wiped to milspec standard, and then reused in a different chassis to assure no user data ever fell into the hands of another user. The process is not daunting by any means.
Replacing the factory 5400 RPM HDD with a new SSD will not only improve performance, and reduce power consumption (and therefore reduce waste heat as well as prolong runtime on a battery charge), but the factory HDD is past its expected five year lifetime by now.
As to data migration, there are multiple drive cloning apps available which make the process practical. However, before you pick up the first tool, I would make a backup to an external drive, network-attached computer, or the cloud, and verify the backed up data matches the source; then, repeat the process to a different external drive or a different cloud provider.
Note: Do NOT shop for an NVMe SSD as those are incompatible; you would want a SATA-III SSD.
No, you would not see a maximum speed difference between an external HDD versus an external SSD due to the USB ports limited to a maximum of 60 megabytes per second (or 480 megabit per second). You may see a quicker response time (or latency), but this is in milliseconds and would be very negligible to the average user. I would buy an external HDD because they are cheaper per gigabyte, but if you want a rugged drive then SSD's are better because they don't have an arm that reads/writes the data. If this is just a home laptop that doesn't move often or ever, then go with an HDD. In my opinion, there is still no speed difference between SSD's and HDD's if you are using USB 3.0 or higher ports (These are typically in laptops or computers made around 2015 or newer).
If you want suggestions on storage, my favorite external HDD brands are Western Digital and Seagate. They are reliable HDD's that are loved by consumers. If you don't want to spend that much for an external HDD, Toshiba makes reliable HDD's and are common to see in laptops.
If you want SSD's, my favorite external SSD brands are Western Digital, Samsung, Seagate, SanDisk, and Crucial. You don't have to stick with these brands, but as long as they are rated high and have NAND Cashe you should be fine.