Support and customer relationship tools recommendations?

Hi all.

My company is growing nicely, but one area we have neglected is tooling around talking to our customers and leads. I know this question has been done to death, and I have trawled through the discussions, but didn't necessarily find what I wanted.

I guess the term would be CRM, but I am looking for something that can allow us to not just use adhoc email and phone conversations as main interface to talk to users. I.e. a customer will email me asking for XYZ, and I will answer it, but there's no real tracking of that convo. I want to be able to see all the communications I have with customers and leads in one place. For sales AND for support purposes too.

I want something that is not so hyper focused on the sales pipeline, and more just about allowing us to manage our relationships with leads and customers in a minimalistic fashion.

Keen to hear peoples ideas and suggestions