To get your website into top pages in Google search m there are a lot of factors involved. One of them and the first I should say is choosing a proper, relevant domain name for your website
Many times companies and businessmen choose their offline business name or something say a site names rmk.com , now it does not really tell what it is about, its just taken from the company name RMK corp, so would classify as a bad name from serach engine point of view unless of course if the RMK corp is so popular it does not need keywords in domain name. Others try to pick something that is short and catchy, which is easy to remember and come back to the site later. This is a major advantage of choosing a simple and relevant name because it makes your customer permanent, they do not ahev to go through the same serach process to get to your page, they can now come directly remembering the simple and catchy domain name.
From the search engine optimization point of view, there are better approaches.
Search engines currently give a significant amount of value to the words in the root of a domain name althpough this strategy is bound to change in future because if lots of fake sites. But as yiu said there are other things google looks for when indexing your page. A good optimization effort might lead to the site appearing high under the phrase in the domain name. So it is important to choose domain name properly.
A simple approach to choose domain name from search engine optimization point of view is to match keyword phrases and domains. What needs to be done is to research the most popular keyword phrases being used by people in your particular field and then buy domains matching those phrases. Taking such a name with keywords would lead to the site being optimized well and obtain high rankings in major search engines. Obviously, keyword phrases with tons of traffic have already been taken. So shortlist the keywords and you will see that many of the key phrases are still available. Build a site on one of the domains and you should find your optimization efforts leading to successful results.
So, All in all, I would advice you to choose a good domain name with keywords to enhance your site's popularity but make sure it is simple,catchy and easy to remember. I think of it as an investment and think you should do that.