What kind of machine do I need to taken in a men's Sewing Machines Parts and Sales in Los Angeles

I want to take in my shirts as I am tall and slim. Ideally I would like to get the cheapest sewing machine possible as this is the only thing I will be using it for and my understanding is this is a pretty basic task.

I would be just creating a new side seam and then cutting the excess fabric following these directions

Can anyone recommend a frugal option?