Pick and choose from multiple videos into 1

I have videos of my kids ballet performance taken using 3 different cameras with 3 different formats. I'm looking to combine them into 1 video. I'm looking for suggestions on a editing software where I can load all 3 videos like on a timeline, line them up, then pick and choose which video will be used for specific times. I'm planning to overwrite the audio so the exact timing is not too important. For example, assuming all 3 videos are lined up so the start of the earliest video (#1) is at 0 sec and the end (#2) is at say 120 sec, I want to be able to do the following:

0 to 10 sec, video 1
10 to 14, video 2
14 to 16, video 1
16 to 20, video 3
...
115 to 120 video 2

I'm willing to convert all 3 videos into a common format if needed. I'm just looking for the software that allows the pick and choose part easier. Thanks in advance.

Edit: I did go through the how to guides, but I didn't see anything on handling multiple files.