To stay within your budget, I can offer up to 5 keywords targeted across your site, sticking to local rankings to help increase conversions.
I can see a short gain in ranking over the next 2 months of work at this budget, but hitting first page will take considerably longer.
If you wanted to see yourself sitting in first, or at least the top 3, within the next 3 months, you would need to look at investing roughly $599/month, which will cover a complete overhaul of your website to help increase SEO friendliness, include up to 12 keywords and increase the amount of back linking that can be done.
Please message so we can discuss further,
Daniel Larson