Continuous Deployment and CI recommendations for SF

I have been working with Sitefinity for roughly a year now, overall my experience has been great except for deploying code. I have attempted to use Thunder Code Sync multiple times, it is a great tool when it works. I have lost many hours  removing and reinstalling Thunder just to get Code Sync to work. I am in search of a more reliable way of deploying code to our servers that is easy to use once setup to replace Code Sync and manual file transfer. I tried using VS publish which caused Sitefinity not to work, but I have not spent time to figure out why.  

I am in need of a more automated way. I have looked a few options, not sure what is the best option for Sitefinity deployments that also could be leveraged for other projects. Something that would integrate with VS and/or VS online, is ideal but not necessary. I have research MSBuild,TeamCity and Octopus, but Octopus is out due to cost and MSBuild seems to something to the code base that breaks Sitefinity. The ideal would be something the team can grow into. I have started the process of getting ​our team to use source control( VS online) which has been a struggle, I do not want to overwhelm the team with a complicate tool for CI/CD.  The foucs is first deployment and then Continuous Integration as we move toward TDD. Our development team is small 4 total (2 devs and 2 data), part of a small IT team for a nonprofit. 

Currently all our servers are on premise hosted in Hyper-V, while we create a plan to move to Azure for non-production servers.   

Sf Environment:
Local dev
Test server
Production Server

Thanks in advance,

Scott