Private accounts

Is it a good idea to follow them if they have a higher follower to following ratio, or should I just stick to the normal account 3 likes and a comment ?

That would be dependent upon your goal for the account. If it's to grow, then I'd suggest you stay away from following private accounts - if they don't accept and leave your request pending, it still counts as a follow for your account. This can lead to a lot of follow space being superficially taken up.

I want to grow my account and get a good engagement. The types of private accounts i'm refering to do not have over 200/300 following and have around 50 to 100 followers.

I agree. If it's a private account and they won't accept your request it will turn out to be a negative thing. Since your goal is to get good engagement, follow public accounts instead. Follow public accounts that are within your niche and use hashtags correctly.

Loren