Possible to get #1 on ALL those keywords with almost no investment? No way. You're not going to knock off apartments.com and rent.com (both PR 8 with millions of backlinks) without serious money. Could you get #1 on one of those keywords? Maybe, but you'll spend a ridiculous amount of time, and if you attain #1 then one of the other companies will spend some serious money on SEO to knock you back off. Just trying to be honest ... not trying to detract you. Try to be more specific to start with, you'll get far more hits than trying to optimize for a ridiculously popular keyword.
Is it possible? Sure, it's possible to get the #1 ranking for ebay with enough effort, but highly improbable. Someone searching for "apartment" is a bad searcher or probably not going to convert anyway, think in larger search terms that an educated consumer would use to get what they want and target those phrases. The rest will come naturally. Now if you want an SEO contest, take over the number one spot for Ebay. The SEO world would bow at your feet.