You can start from DigitalOcean for just 5$/month and expand later when will be required if project will take traction.
Talking about the focus - do not try to attract any person in your city or country interested in pets, choose a single topic instead and start with it, for example - dogs only.
When you have a lot of visitors and you know your target audience you can make money by ads or promoting any content which will be interested to your visitors.
But before that you have to build an audience first. Find people who are interested in dogs (if you started from dogs). To do so create unique content about the dogs. Write articles, make video tutorials, etc. Post on Twitter, share on Facebook and other local resources. Add Google Analytics for free.
Find local animnal shelters, independent rescuers and other pet care service providers.
Sometimes people with pets need to leave their animals somewhere or to find a person who would take care of them. Help those people find local dog walking, pet sitting and other service providers. Both Animal Shelters and private businesses would be able to have an additional income and you could take your %
Very often people are investing into something only because they are interested in. It is also very common for non-profits. Quora, for example, doesn't have business model, nevertheless, Wikipedia founder Jimmy Wales invested in Quora only because he likes it.
Every NPO always should remind everyone it status and ask for donations.
Another type of donations. Phone cases, T-shirts, cups and everything else. For example, here is LibreOffice shop
This comes together with #2. If people are intersted in your content, you can sell professional payed only content and provide inhouse trainings.
Now you can take other topics like cats and expanding your IT infrastructure.
To be honest, there are many ways in the life to earn money but these points I provided are general principles how it is done.
Bonus tip: you, of course, may build a team, found a startup and make a lot of money, but this is going to be another story...
Build something people care about and would love with whole their heart. People are giving their money not because corporations are asking for so but only because they want. This is the key to success of any business and especially NPO and open source projects.