Yep.. you could easily top in search engines even though your site is newly made. Link building is the key to your success. It will only take 2 to 3 months of waiting. But if you're still thinking of making a website, you should put your target keywords in your domain so that you can actually rank higher for atleast 1 to 2 months...
Depends on the level of competition on a keyword.Low competition Keyword would not take more than 3 weeks to rank your site,but high competition keyword will take at least 3 months to rank your site.
I think ranking in top 1000 is less difficult then maintaining a constant position in search results. New sites have a "New Content Boost", therefore you will be able to see them in top 1000 or even top 10. But new sites only rank well for few days, and then they get lost in search results. In order to improve new sites rank, get high quality and relevant backlinks
BACKLINKS - not only just backlinks; you need quality backlinks for you to be in top 1000. PATIENCE IS A VIRTUE.
It's definitely worth doing some research on the keywords you are interested in. Check competitors, find out how many pages have the keyword in title tags. I also agree with other posters that quality backlinks are crucial to gain decent positioning. Unfortuantely a large part of your hard work will take some time to be reflected in Google. Good Luck