Which CRM is suitable for these needs? Small NGO

I work for a small NGO and i've been given the task of implementing a CRM system to keep track of our partners.

One way of income for our NGO is making partnerships with businesses who want's to look into sustainable solutions. When a businness decides they want to be a partner, they will pay a yearly subscription. We will then invite them to network dinners that can set them up with other sustainable businesses, host talks and workshops about sustainability in their field and so on.

Now we have so many partners (40+) that it's hard to prioritize and keep track of our interaction with them. Some partners are very large coorporations who pay way more in subscription than the small partners. So on one hand, we want to reach out personally to all of our partners on a reguar basis, but obviously in a way that reflects how much their subscription costs.

I'm looking for a CRM that lets me:

• Create a list of all partners and potential partners
• Log all information about that partner (phone, mail, main contactperson), and also all interaction with these partners. Let's say i've met a partner at a conference and chatted with them about a new solution. I wan't to write that in the log, so I can look it up when I contact them the next time. Or maybe i called them to ask if they wanted to participate in a workshop. You get the idea.
• I want the CRM to email me when no new logs has been made for different intervals of time. Let's say 3 months for a small partner and 1 month for a big partner. That way the program will remind me that i need to interact with different partners.
• I want to sync the CRM with our MailChimp newsletter, so that when I log a partner into the CRM the first time, i can easily click a button to send them a "Hey, happy to link up" mail and then add them to our MailChimp newsletter list.
• I want the CRM to be easy to operate and access. We have a lot of voluntary students working with us, and if they go to a conference, they need to find it easy and manageable to create a new log.
• We have a low budget, so something cheap or even free would be preferable.

I'm totally new to CRM. I've heard the names "HubSpot" and "PipeDrive", but i've understood that they are very oriented towards closing leads. But we never want to close a lead – we want to stay in contact with our partners and keep them subscribed.

Thanks in advance.