“Apartments <city>” is going to be really competitive because of the high finders fees people can get when someone rents an apartment through them. The first page when I search in my city is mostly companies that locate apartments online exclusively. For reference, craigslist is 9th and there’s not a single complex listed until 18th.
I could be wrong, but I don’t think you’d want to put in the kind of money it would take to bump into the top 10 for that search in a metropolitan area. Maybe you’re in a small town and it would make sense, what are you seeing on that front page? Other similar sites?
The smarter money might be in going more specific, something like ”<neighborhood> apartments”, <street> apartment”, ”<college> apartment”, or ”<employer> apartment”. The thinking is you don’t get the volume of traffic from terms like those, but it is the right traffic for your purpose and maybe even folks who are looking for a way around the locators on the front page.
Have a strategy figured out when you’re building content for the site if you can. You don’t have to make it sound corny and robotic, but it helps fill in some blanks and make decisions in other areas as well.
My quick and dirty SEO speech for clients usually says there’s one part that you can do when you build the site by including the strategic words you’re going for in prominent areas (don’t forget the URL) and making sure the site is easy to index.
The other part is more of a commitment and ongoing. You have to build fresh content, find ways to get links to your site, and keep it moving just like you would any other kind of marketing.
There’s no magic way to the top unfortunately, just applied strategy and time.