Switching MBP from hard drive to SSD
You can "restore" to a new Mac during setup from a Time Machine Backup. This would be the most straight forward solution, but it won't let you selectively pick and choose what to restore.

An option still involving Time Machine would be to exclude locations that you don't want to backup and restore fully (such as the Applications folder) and just backup that folder manually onto some external hard drive.

A clean way would be to just install Mac OS X fresh onto that hard drive and copy everything "by hand". This gives you most control over which files will be copied and which you don't need anymore, but it'll take you much longer.

In regards to how to do it all (install Mac OS X onto your new SSD hard drive), I would consider this:

Currently I assume you have three hard drives. The first one inside your MBP (the internal hard drive). The second one in your external hard drive (1TB Seagate with the Time Machine Backup on it). And the third one is your new SSD (currently not in any case).

OPTION 1 (if you can't tinker with your external hard drive)


Attach the external hard drive (Seagate) to your MBP.
Partition the drive into 2 partitions with Disk Utility (hopefully this will work without having to erase everything)
Install OS X from your MacBook Pro directly onto the external SSD drive. You probably have to download the installer again and need to select the correct install target partition during the setup.
Build the SSD into your MBP.
Start the MBP while holding the OPTION key then select the external OS X partition (also well explained here: http://osxdaily.com/2014/10/18/clean-install-os-x-yosemite/ - this also applies to El Capitan)
Now repeat the OS X installation procedure onto your internal SSD drive
Restart the MBP and hold OPTION again, this time select the internal SSD
Restore with Migration Assistant or manually.


OPTION 2 (if you can't partition your external hard drive)


Install the SSD drive into the external hard drive case (switch it with the external hard drive)
Connect the external hard drive (with SSD inside) to your MacBook Pro through USB
Format the SSD to whatever you prefer and Mac OS X supports (HFS+ usually)
Install OS X from your MacBook Pro directly onto the external SSD drive (over USB)
After installation is completed build the SSD from the external case into the internal MacBook Pro (this is the first and only time you open the MBP).
Put the second (external) hard drive (with your Time Machine Backup on it) back into the external hard drive case (to connect over USB).
Restart the MBP and connect the external backup over USB, then start the Migration Assistant, which will let you restore from a TM Backup.


Alternatively, you can also put your original hard drive from the MBP into the external housing in Step 6 and just copy everything manually (and skip Step 7).