VIF Vs Mutual Info

Question

I was searching for the best ways for feature selection in a regression problem & came across a post suggesting mutual info for regression, I tried the same on boston data set. The results were as follows:

#feature selection
f_selector = SelectKBest(score_func=mutual_info_regression, k='all')

#learning relationship from training data
f_selector.fit(X_train, y_train)

#transform train input data
X_train_fs = f_selector.transform(X_train)

#transform test input data
X_test_fs = f_selector.transform(X_test)

The scores were as follows:

Features    Scores
12  LSTAT   0.651934
5   RM  0.591762
2   INDUS   0.532980
10  PTRATIO 0.490199
4   NOX 0.444421
9   TAX 0.362777
0   CRIM    0.335882
6   AGE 0.334989
7   DIS 0.308023
8   RAD 0.206662
1   ZN  0.197742
11  B   0.172348
3   CHAS    0.027097

I was just curious & mapped the VIF along with scores & I see that the features/Variables with high scores has a very high VIF.

Features    Scores  VIF_Factor
12  LSTAT   0.651934    11.102025
5   RM  0.591762    77.948283
2   INDUS   0.532980    14.485758
10  PTRATIO 0.490199    85.029547
4   NOX 0.444421    73.894947
9   TAX 0.362777    61.227274
0   CRIM    0.335882    2.100373
6   AGE 0.334989    21.386850
7   DIS 0.308023    14.699652
8   RAD 0.206662    15.167725
1   ZN  0.197742    2.844013
11  B   0.172348    20.104943
3   CHAS    0.027097    1.152952

Could you please help in understanding, on how the select the best features among the list.

Thanks in advance!