I think shutters would be good to visually break up all the brick but I think reddish brown shutters would not provide enough contrast to the brick. I'd be inclined to do light gray shutters and a med. gray door (possibly grays with blue undertones).

I think a navy door would look lovely or a turquoise would be very welcoming and bright. Either way, I would go with white shutters or none at all so your home's facade is appreciated, vs just noticing the shutters.
Then with the money saved, I would instead add some landscaping. We took a picture of our home and went to a garden center during a slow time and they worked with us for free, suggesting plants/bushes and where to place them, etc. and then we were able to use the plan over the course of building up the garden.

1920's Remodel and Basement Extension · More Info

Here is a mock up of the dark red/brown shutters with a navy door and, as others have suggested, a gray shutter, which I paired with a medium dark red door.

I tend to lean towards the gray shutters. which you could pair with either door color.

Hi Inez Grider

What about a color like Black Plum? Or even a medium blue like the one in the picture below

Hi Inez. Great house! Since you can see where the outline was of your shutters, that would suggest the house could use a cleaning to even up the brick and mortar colors. I like the idea of darker shutters with a brighter door so you have some contrast against the brick. Black plum as suggested by Timberlane sounds like a great option. Good luck with your project!