You've made an investment in hopefully original art that supports local artists. This purchase was made from your heart and not to match your sofa or decor.
If you have bought a piece of art on paper such as a hand pulled print, watercolor, or drawing it will need to be protected under glass. A matt is cut to keep the glass off the surface of the artwork and this can be made as simple or as fancy you like.
Consider the following:
The exposure to sunlight. Water colors and prints should never be hung in direct sunlight. UV glass can be purchased to add further protection to items from damaging sunlight.
Abstracts and non representational art is acceptable for any room in your home and can be beautifully combined with antique furniture. What activities occur in the rooms where you will hang your art? Is the art calm or exciting? Will the art be hung in the public versus the private areas of your home?
The size of your wall with the size of your painting.
The ease of viewing art in museums. Museum measurements: 59" from the floor to the center of the painting. This is a helpful guide to keep in mind in hallways and large open walls.
Furniture placement: a painting above a sofa or buffet should be low enough to feel connected to each other when viewed from the center of the room. A painting hung near a chair, table, or lamp should be low enough to enjoy while sitting. Likewise, when hung near a bed or bedside table should be low enough to be visually connected and enjoyed while laying in bed.
Don't forget to put art in unexpected and smaller areas. Small works are meant to be viewed up close and intimately. You will find such areas near doorways, the stove or sink in the kitchen or near the mirror in the bathroom.
For wall collages consider subject matter (common theme) keep the frames similar.
Above all break any rule to enhance your personal enjoyment of the art.
It is my hope this makes you feel more confident in purchasing and hanging artwork with satisfying results.