CRM for contacts? Cold emailing? How to proceed?

Yes, for sure, there're many tools on the market that can help you to do this.
You can send your email sequences with follow-ups and build lists with snov.io.

Good initiative @uifort

I can see Pipedrive on the list so I would recommend two alternatives for your comparison: HubSpot CRM and Streak. Why?

1. The free tier is good enough for early-stage startups
2. Easy integration with Gmail and allows you to keep track key statistics
3. You can easily create templates and follow up actions all in one place

I'm using these tools to get a better clarity when doing cold outreach for my side hustle, it works pretty well so far. Happy to exchange ideas.

I think PipeDrive will be a good fit
https://www.pipedrive.com/

I work at a CRM company, and can assure you that nearly all CRMs can accomplish what you're looking to do. Here's the way I'd do it using my CRM (amoCRM):

-Define the stages: What steps does each lead go through? In the CRM, name the stages of the pipeline to reflect it (1st email sent, need to follow up, in discussion, etc.). Plan this so that a lead is always moving forward or paused, never moving back.
-Prep existing leads: Clean up the email list you've already got in a spreadsheet. Add a column for the stage that they're currently in and define it for each lead.
-Import: Upload the sheet to the CRM, which will also sort your leads into the right pipeline stages.
-Add templates: Write your template emails for each stage and add them to the CRM
-Automate: Add what needs to be done at each stage. In amoCRM, you can add automations that assign tasks, send emails, add tags and more. For example, when a lead lands in the 2nd follow-up stage, send the 2nd follow-up email automatically.

Of course we offer many other features (like the ability to chat with leads in messaging apps), but it all depends on your needs. Our team also gives free 1:1 set-up sessions if you need some help.

For cold calling, you should use lead gen tools IMO.

I've been using a tool called SalesBuddy.
Might help you, check it out. http://bit.ly/2sQgtzn

There are a ton of CRMs on the market. I've built a few for myself over the years and you could always use something a little lighter weight than most, for example, Podio by Citrix, which is cheap, easy to configure/maintain and browser-based with a complimentary app. You can do a lot with it and their licensing is straightforward and support is good.

As far as reaching out, my experience has been more positive with cold calling vs. cold emailing, but your mileage may differ.