An SSD does have a speed advantage over a standard hard drive, but you typically only notice the speed increase on things like initial start up and when searching the hard drive, or running software that uses large amounts of virtual memory, such as photo and video editing software.
I think you misunderstand how the replacement hard drive will be installed. If you just go to the store and buy a hard drive and install it in your computer, when you turn on your computer it will tell you it cannot find a boot device. So, what you have to do is either install your computer from scratch (hopefully your computer came with recovery disks) which will make the computer like when you very first brought it home. So, if you bought the computer with windows 8 and you do the recovery, it will have windows 8 even if you upgraded to windows 10 on the old hard drive.
There is also a method of transferring your current data to the new hard drive, typically referred to as a "ghost". the advantage here would be that you are going to get your computer exactly the way it was with the old hard drive, all your data, all your programs, etc. The problem with this method is that if there are problems with the old data, you will still have those to... only they will run slightly faster.