What's the preferable encryption for large data and files in terms of speed and security other than AES? First of all, I'm relatively new to encryption so please bear with me.
I'm looking for a way to encrypt large amounts of data only on my device, no need to transfer my encrypted files/data (10-20GB or less), I don't really care about speed as long as the encryption is really strong. I have tried encryption with AES-GCM and using RSA for encrypting the AES Keys, but AES doesn't really give me that safety feeling like it's only 256bits maximum.
Based on your comments I have a feeling that may be you don't really understand what a huge number of combinations a 256-bit key means. At the first glance 256 bit is &quot;just&quot; 16 bytes. But look at it closer. With 256 bits we can encode $2^{256} = 10^{77}$ numbers. It is 100 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 numbers.
Still too theoretical? You may get better feeling if you run a simple Python script:
i = 0
while i &lt; 100000000000000000000000000000000000000000000000000000000000000000000000000000: # 2^256 ~= 10^77
    if (i % 100000000 == 0):
        print i
    i = i + 1

Every second, on weaker CPUs may be every 10 seconds, you will see a 9-digit number. In 1 day you will see the numbers are 10-digits. In 100 days you will see 12-digit numbers. In 3 years you will see 13-digit numbers. If you pay for 1 000 computers for 30 years, then you will get 16-digit numbers. Still extremely far from 77-digit numbers.
This script is very simple and fast. But brute-forcing of AES will be much slower. For every key candidate one would need to decrypt some considerable peace of data, then analyze if decrypted data mean anything like document, image, video.
Be realistic. Estimate how much money would an attacker obtain if your files are brute-forced and if they can sell your files to somebody. Will they get \$1 000, \$1 000 000? Nobody will brute-force your AES password (except checking against dictionary with typical weak passwords and their variations, which is very quick). If your secrets are worth \$1 000 000, then it may be much cheaper to pay hackers $500 000 to break into your system, read your passwords or install key loggers; or install spy cameras in your home, your car etc. and thus get your passwords; or steal your key if you have hardware token.
TLDR: AES with 256-bit key is more than sufficient.