I have little experience with video editing. I do know (from seeing many questions here on Tom's) that video editing typically needs a fairly powerful machine with a lot of RAM. Does that mean a cheaper machine will work if you are just patient with how slow it is? I don't know. I suggest you read a lot of reviews of the editing software and see what they require for running. Sorry I can't be more specific.
BTW, I just bought a new laptop for $2k+. It has a separate graphics engine (which cheaper machines don't have). If I wanted to do video editing, the recommendation was to upgrade two levels on the video engine for several hundred dollars more. That would be for "pro level" editing but kind of gives you an idea. If your editing is just cutting and pasting, that is not so intense.