What I basically want to do is, perform a test on my Wi-Fi and brute force it instead of a dictionary attack. I googled, and all of them showed me examples of dictionary attack and no bruteforcing.

My password is somewhat like this- aXb2@abc.

I know this can take a lot of time, but since it's my home I can let my computer do the work. Also, is there a better option than bruteforcing this type of passwords?
I am using Kali Linux 2. Thanks. 

No, you cannot determine how close you guessed looking at the hash. A hash function is designed with this in mind: one single changed bit on the input must change a lot of bits on the output. Its called Avalanche Effect.

Bellow are SHA1 hashes for some of your example passwords:

cbfdac6008f9cab4083784cbd1874f76618d2a97 - password123

b2e98ad6f6eb8508dd6a14cfa704bad7f05f6fb1 - Password123

2b4bfcc447c3c8726d26c22927a68f511d5e01cc - password124

115b55dcc1cd9a0dfdd60c120e83eaf658c45fc6 - right horse battery staple

abf7aad6438836dbe526aa231abde2d0eef74d42 - correct horse battery staple


A single bit change will completely change the hashing result. In fact, in an ideal case for every bit of input change every bit of output will be changed with a 50% probability.
