From my experience, ranking is not as easy as people want to make it. I found this forum after multiple failures and got my breakthrough here after advise from a member.
Just ask yourself, how soon can a student be more versatile than his teacher? Let us assume that you can write very well. What about technical seo that has to do with how well the site was made? Writing good articles is not enough, the structure of the site is also a top determining factor.
You can replace money, but you cant replace time. I leant this the hard way. The time you will waste trying to see if your site was well built to beat the old gurus, you cant get it back if it fails. But the money you spend buying a good site can be replaced if you fail.
If i were you, since you say your budget is small, I will look for a cheap site that is well built, buy it and get more help from the seller or others to make it even better, then continue writing on it. This was exactly what I did after wasting about 6 months trying to build a site by myself. That was the best investment I did in bloging. Now i have 8 blogs