Hi, Melissa.
Buing backlinks is not necessary. To answer your question completely, I would have to know more about your website. But, I can offer this with certainty:
1. Be sure that the anchors of your backlinks match your key term or word for your page. In other words, if you sell oranges, and this is your key word, then be sure that the anchor, or title, of your backlinks is "orange" or at least contains that key term.
2. There are two reputable sites that offer link exchange services. I recommend both of them. They are:
linkalizer[dot]com and linkexchange[dot]com.
3. Building up many good back links and a good reputation takes some time and ranking a new website takes some time, also. Just like a new business in real life, to succeed usually takes persistence and hard work. There are no short cuts.
Regarding buying links, I strongly advise against doing this, because Google considers this unfair and may consequently penalize your site, and it is just not necessary.