Hi and welcome to DevOps SE!
While DevOps is not self-purposed, maybe it is worth to step back for a moment to find out the actual problem before trying out solution.
As you have asked a more or less generic question, I'll give you sort of a "DevOps primer" stick more to methodology rather than give you a list of tools.
How detailed you would tailor the implementation of this depends on many factors like business needs, complexity of teams, products and systems. .. and the time you have got/are allowed to think.
- Why did they ask you to update DevOps techologies?
- What is the business objective i.e. what will change after you are done - find out the management perspective. Will be software delivered faster/in shorter periods, or are deployment problems a real issue?
If there is an update of DevOps technologies, what is the current DevOps toolchain (please read on this Wikipedia article to understand families of tools by their purpose in the toolchain) your colleagues use?
Who i.e. which team members have knowledge/daily usage of which of these tools?
- What are technically software products your manufacture and deliver?
Now you know the problems and the existing toolchain and products it produces:
- Are there now some quick fixes to achieve quick results or do you need more time to analyze data you have now, and find answers to questions you have to the team and management?
- Which tools do you think are missing and how which change would bring the company closer to the set objective?
- Will be free open source tools enough or some enterprise licenses could be required?
- Is it possible to design a DevOps strategy and generate iterative tasks to deliver changes and improve the situation in baby steps (design thinking with your team as end users or do you have a complex situation in large enterprise - system thinking)?
Side note: regarding to container management, depending on existing expertise you might consider using a solution bundling Kubernetes, e.g. OpenShift as already mentioned or RancherLabs etc. Regarding Jenkins, after you know what is happening, skip through its plugins, Jenkins-as-is is just a beginning.