Having worked with designers, in a frame shop, and currently on staff at an art gallery, I've picked up a few tips to help you choose the perfect fit for your new piece of art.
In a gallery setting, we like to hang art with what we call "breathing room" so that the pieces hanging nearby or objects in the room won't detract from viewing the piece, like a few feet at a minimum. In a home setting, you want to fill at least 50%-65% of the wall's width. Anything over 75% of the wall width and you will risk having art that looks too large for that space.
In a gallery or museum setting, it's standard practice to hang art 60" at the center. Meaning, we measure from the floor up the wall 60" and that is where the center of the art should hang. This allows the piece to be centered close to the viewer's line of sight. In a home setting with 8-9 foot ceilings, you still want to keep to hanging art on a wall (no furniture) that is in line with the viewer's line of sight versus hanging art where the top of the pieces are all in alignment with each other.
It's okay to let objects overlap your artwork, it creates a collected and "full" look. Avoid having your artwork looking like it's alone and isolated, and instead allow it to connect with the furniture and be part of the bigger presentation. You want it to appear as part of the room. You can find many examples of this in design magazines, Pinterest or Instagram of an entry setting over a credenza or a side table, etc. If hanging artwork over furniture, like a couch or bed, aim for about 10-12" higher than the top of the furniture.
Lighter pieces typically look their best on a toned wall so the edges can be visible and not disappear into the wall. Similar to finding a mat color when framing, you want to find a wall color that coordinates with secondary or tertiary colors, not the main color itself. This creates a compliment to the main color, instead of creating competition with it or worse: a slightly "off" color that will only clash.
Some like to move artwork around their home until the piece tells them where it would like to be. The right piece in the right spot will shine and it will become obvious to you so have fun experimenting with many locations.
p.s. Don't forget to give your new piece of art some great lighting...it makes a BIG difference!