"modernize"?....You mean with a "modern" rug?
Don't think it can be done....and still look right.
Why not do that strange thing and buy a solid color rug with a bit of texture...in a color very near...or at least the same tone as the sectional in the den. Not going to add color....but you do that with accessories.
And I would forget the drum light fixture....How about lowering the one you have on a chain? It will be right with your house and add another dimension to the room.
Curtains...canvas in a color very like the rug....perhaps with a trim stripe of grosgrain...
And a BIG solid color vase on the floor....maybe burgundy...or a jade green....perhaps even a Weller sort of brown.
A runner in the color of the vase....with a heavy glass "thing" in the center...modern in style and heavy glass.....and brass or silver antique candle sticks...in the style of the table.

Here is a link that might be useful: rug

I suggest you post some pictures here so folks can see your space.

Also take a look at the Houzz website for inspiration.

And furniture companies that sell that style furniture (new) are likely to also have some images showing their furniture styled in an up to date way.

Ethan Allen, Stickley, Drexel, Henredon.

Aso Traditional Living magazine, and Souther Living may give you some ideas.

Rugs are very hard to select, because the way they play in the light is so dependent on your home and its lighting.

Ditto what Linda said about the chandelier. Is the neo-gothic monstrosity original to the house? If so, you really should keep it. If it is not, okay, replace it -- but a drum shade? That's MCM Revival and will look dated before you sneeze. They've been around a few years now and HD is starting the carry them, so they're on the way out.

You already have a Craftsman room and Queen Anne furniture. If you throw in anything that's too modern, you will have three styles in one room. It would be better to match either the home style or the furniture style or go with something pretty neutral. Otherwise the room will look like it's suffering from ADHD.

As Julie said, pictures would help us a lot.

An Oriental rug seems like the best choice. Preferably without a central pattern.

An Oriental rug seems like the best choice. Preferably without a central pattern.

I think if you post some pictures of your rooms and furniture, you're more likely to get some specific and helpful advice.