Build a Website and include social media feeds

I need to re-do my research group's website: [login to view URL] Make it look simple and need. Apple style. Easy to maintain (by myself). Need to be in a language/software that I can manipulate for future updates. Should be able to include a web counter (stat counter). Need to be mobile friendly (smart-phone, tablets, etc.) Just created a twitter account that would like to link it to my website to show pictures of events me and my students participate in. To make it look as it is now if possible (timeline on the right side). Would like also to show updates of the Facebook account of the student chapter I advise, to be able to show pics, events' advertisement, etc. Need the source files once the project is finished to be transferred to our Department's host server. I am open to discuss on the phone for further details. I am open to other innovative ideas. Would like to see portfolio of previous work if possible.