What are your recommendations for getting rid of weeds and grass that's grown over a garden plot? I recently purchased a house that came with a fenced in, on the ground, garden but it's gotten a bit overgrown.

Cleaning up the weeds with some good ol' elbow grease has been working so far, but I want to make sure that the weeds don't grow back, at least to a meaningfully bad degree. I also don't know if this is the best, or even a good method since I'm new to gardening.

I was thinking of putting down some rolls of paper where I don't want any plants but there are so many options and I don't know which to go with. Advice on that route would be appreciated as well.

Thank you in advance.

Edit: I just saw a different post here about starting a garden plot from grass which sounds relevant to my issue. I'm leaning towards fallowing the plot and tarping it this growing season and trying again next cycle.