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As far as I know, Google recognizes 301 and follows them. So your new URL should rank automatically after some time in the SERPs. Also the link juice from the old URL will follow to the new one, if you choose a 301 redirect.

I am trying to rank with my page on a major keyword for my E-Commerce store. Currently, I am ranking on page 4 in SERP:
mydomain.com/category-for-major-keyword

Now when people like to link to me, what should I do? Shall they link to:

1. mydomain.com or
2. mydomain.com/category-for-major-keyword

What brings me more in terms of ranking for that keyword with my category?

Thanks, Robin