Hi Matthew!
Link building in today's SEO world is about relevancy, trust and authority.
The guest posting option is fine (asking blogs if you can write something for them), as long as what you're writing is an original and quality piece of content, and you're reaching out to trustworthy blogs that are, ideally, closely topically relevant to your own site for a link. In a perfect world all your links would be from relevant domains. However, links from irrelevant domains aren't bad - they still pass trust and authority, and having irrelevant links is part of a natural, diverse linking pattern. But if all or the vast majority of your links are from topically irrelevant domains, that becomes a problem.
I use Blogger Link Up and My Blog Guest to find prospective blogs to approach, but do your research, make sure you are reaching out to quality sites. Consider creating other content besides articles as well that stand a good chance of getting shared. Videos and ebooks for example.
Although having a peek at competitors' link profiles might give you some good ideas, don't just copy everything. Again, you want only quality links - links from relevant trusted websites to your own. So don't try and copy anything that doesn't meet this criteria.
You want your links to resemble a natural link building pattern and that gives you the biggest clue as to what is acceptable nowadays - so from a variety of sources, using a variety of linking/anchor text including the URL itself as you'd expect if they were just creating from people sharing your content around, and in a natural context (e.g. part of a review, or a resource link in a genuinely useful comment on a relevant article). Be very careful about deliberately creating links with your exact keywords in the anchor text. For example, if you were targeting the keyword 'car wax' you'd be better off linking to your site with natural variations such as 'here's a great article on car wax' 'here's how to apply car wax' 'the pros and cons of using car wax'. I think anchor text carries a lot less importance nowadays and Google will take more of a signal from the content on the linking page and linking site (but on the other hand, if you create lots of exact-match anchor text links to your site, Google does then pay attention as you risk a penalty). So yes, get natural-looking links from authority websites in your niche and you should see an improvement in your rankings for your target keywords. Link building aside, focus on creating great content first and foremost, because in time that'll earn you natural links anyway.
Your second question - if people start talking about your article and sharing it, yes they will just share a link and that's what you want. You don't want them to share the actual content of the article. There would be loads of duplicate copies of your article all over the web then, and that's not good for SEO! (sorry if I have misunderstood this part). Getting all those social shares is good though, it's sending a signal to Google that your site has something worth sharing, that perhaps it's an authority on your subject.
Hope that helps a bit!