Will my system be able to handle full disk encryption?
Solution 1:
Performance
Disk encryption will lead to a small yet measurable performance decrease since the computer needs to perform an additional step during disk access. However, the bottle neck on a system with specs like yours will almost always be the disk itself and not the processing power required for encryption or decryption.
If you encrypt less data (e. g. only the home directory instead of the whole system) the performance difference will be smaller for obvious reasons. This only applies if you use the same encryption scheme in both instances! The home directory encryption offered by Ubuntu will use eCryptfs as opposed to dm-crypt for full disk encryption. The former is known to be slower than the latter but offers more flexibility (i. e. encrypting only a subset of files on a file system and with different keys, e. g. for different users).
Major problems
You'll lose all encrypted files if you lose the key or password (e. g. due to forgetfulness, a partial disk failure, or a mistake during repartitioning). Therefore it's very important to back up the key file and keep a note with the password in one or (better yet) more safe places. The key file is not the same as the password and neither can substitute the other. (In fact, the password is used to decrypt the key which is needed to decrypt the data.)