Snippets on the homepage

I’m looking to use snippets of posts on my blog homepage. The only way I can find to do this is using the_excerpt function in the index.php template. The problem is that it puts a (…) at the point where the excerpt is cut off.

Instead of having a (…), I want this to be a link to the full article and I want the link to be text that I choose.

Is there a way to do this in WordPress?

Thanks,

Leigh