Patch together a video

We have 3 videos (in MP4) format that we'd like to splice together. We know exactly what we want to have done (different points in the videos, etc.). We then want to overlay some graphics and text (e.g., logos + the title/name of the person talking). We want it to look slick, smooth transitions, etc. So need someone with a design eye as well as the ability to patch these videos together.