Even if you are just starting out, building out a customer relationship management tool will help you now and give you a good foundation for the future.
They are especially useful since non-profits operate with a good deal of scrutiny. We are constantly looking for new funding sources, need to keep up with current donors, need excellent internal communication plus deliver on their mission. Plus, non profits often operate under tight regulatory scrutiny.
Some CRMs out there such as salesforce offer discounts or sometimes if you qualify, their product for free. However, for most non-profits, there are some quality CRMs everyone can use for free.
If you have a small non-profit that could scale, check out Zoho (free if only 3 people are using it). This has not only great sales functionality, but also great reporting, invoicing, task management, etc. This is the best to scale.
Insightly (free for 3 people, and just 7$ per user after) may also be quite effective. The interface is not very smooth, but it integrates very well with google and could be the most powerful bang for your buck if you do scale later.
If you have less than 2,500 contacts and just need 1 user, Leadsius is incredibly powerful. There is a lot you can do with it and yet it remains fairly intuitive if you have used CRMs in the past. However, you need to scale later, it starts at $295 per month.
As a final note, you have a limited budget, Nimble is the best as far as increasing efficiency – especially if you are active on social media. It also can integrate with a lot of online tools and is the most proactive. It costs just 15$ per month per user for everything. In any case, with a 14-day free trial you can plug in your databases from Facebook, Twitter and LinkedIn to see their insights.