Should I get backlinks to my website homepage or to pages on my websites?

[Tyler]

I have a small website that I am trying to get on the first page of google for the keyword how to promote your music. I was wondering how long it takes for back links to be indexed by google and if I should get back links to my website homepage or to specific pages on my website.

[Jake]

Bearing in mind that you want to have a 'natural' link profile in order to not be penalized by the search engines, a mix of home page and inner page links would be normal, usually you would have a page link to you page most relevant to the initial page.
Some paranoid about having to remove links remove or relocate pages getting bad links after an "unnatural link warning from Google" avoid having all but the most solid link sources link to their home page which can't be deleted.
They spider links in a couple of days or sooner, might take longer to effect search results.

Backlink reporting services like opensiteexplorer.org will be slower in finding such backlinks, Google is well know to only report a fraction of the linking sites with a link:yoursite search.

You should have a lot of different target keywords, some sites get the majority of their search trafic from unique never seen before long tail keywords.

There are tools that automatically report ranking for a list of keywords, use the Google tool to find more target keywords:
https://adwords.google.com/select/KeywordToolExternal