No, don't do it. Your house is one of the few that have survived the paint brush massacre!
You have a 140 year old house....paint will not update it, it will destroy it's unique character. Instead, paint the walls a nice neutral color and impose your style in the way of furnishing and accessories. No need to even match the furniture wood tones to the woodwork.
Think of painting your rooms in shades of white. This is not to say paint your walls white. Shades of white, for example, would be like taking a gallon of white paint and adding a cup of blue paint. That will give you a blue hue to the paint and would work great if you are decorating in blues. Same with all other colors...except red, because you will get pink undertones.
You may want to paint your ceilings with a color like Benjamin Moore's Vanilla Ice Cream if you do not paint them a bright white. Older homes typically have low ceilings, so bright white may be a good choice.
Give your woodwork a good cleaning and maybe even it could use a coat of satin finish polyurethane. But, painting...nope, no way. Please don't.
I understand your desire to update, I do. I considered painting my stained woodwork ten years ago and I am so grateful I did not do it. Once you paint woodwork, there is no turning back.
But, if you do decide to paint, you will need to sand it all down, paint with a good stain blocking primer and then paint with your wood trim paint color, preferably in a satin sheen. If you absolutely must.